I eventually got Electrum to broadcast the child transaction, by manually setting the Fee to 1.1 mBTC whereby it worked as regards broadcasting ... but I shall see how long it takes for the low Fee to be mined, considering that it's now averaging 0.6 mBTC per parent or child.

I don't understand all this completely, but my wild guess is that Electrum's step 2 is not working properly, and I had to get rid of the negative number in Output Amount which Electrum automatically had put in.

What is most frustrating is that Electrum did not allow a higher Fee to increase the probability of it being mined more quickly.

What is also clear is that Electrum needs improvement.  For now, here is a solution for a problem which I would think a lot of users will have.

I'm still hoping that some expert(s) will help explain some of the above questions, just to get a better understanding of how CPFP works in Electrum.

I believe that Electrum might now be broken for Child Pays For Parent (CPFP), maybe under current network conditions. It gives me error messages, it fails to broadcast the CPFP with an error message even when I accept the automatic default, and it doesn't allow me to change anything successfully within the CPFP step-by-step process.

Below is a practical, step by step example with the latest Electrum, version 3.0.3

I have Googled and otherwise searched for days and still not found a satisfactory explanation of some of the details of CPFP which may be helpful to know in practical step-by-step usage of Electrum.  Maybe I/we could write some documentation to submit to the Electrum webmaster, if anybody can figure out good answers here, and if Electrum will work in this case.  In doing so, we would be creating documentation and an example for others with this problem, and help promote the usability of the cryptocurrency system.

The problem I have, which is the same problem so many other people have, is that I have a stuck "low fee" transaction, for 6 days now, due to a too-low fee sent by my previous wallet, Multibit Classic, of 0.1 mBTC.
This transaction has no "replaceable fee".
I downloaded Electrum 3.0.3 and transferred everything to there, which brought up my low fee stuck transaction which I had tried to send with Multibit Classic.  (Of course, I have not used Multibit Classic again.)  The Electrum wallet inherited this low fee stuck transaction, did not create it.  However, I'm trying to fix it with Electrum, as other people have said I could by exporting from Multibit Classic and importing into Electrum.

Here is my experience with Electrum 3.0.3 below. I have images for all this, but this forum won't let me post them, but it should be clear enough below.

Under Tools -> Preferences

Use Dynamic Fees = checked
Edit Fees Manually = checked

In my current wallet:

I have an Unconfirmed low fee transaction of 27.5 mBTC
I still have another 10 mBTC in my wallet available
[the two obviously total 37.5 mBTC]

Right-clicking on the low fee transaction, I choose "Child pays for parent" which gets me to a screen which says this:

"...The proposed fee is computed using your fee/kB settings, applied to the total size of child plus parent transactions. ..."
[I assume they mean the fee/kB settings I type below that, because I didn't see any fee/kB "settings" anywhere else in Electrum, including not in preferences. Maybe they mean "submission below" instead of "settings".]
The only thing you can edit on this screen is the Fee.

Total size: 416 bytes [which is the total of parent plus child]
Input amount: 1.2 mBTC [what is this, and where did it come from?]
Output amount: -1.00349 mBTC [what is this, and where did it come from?]
Fee: 2.02349 mBTC [this miner fee is calculated by subtracting the Output from the Input amounts, for some reason -- why?]

If I click OK on these defaults, without changing anything, I get an error message, "Max fee exceeded" -- yes, on these default settings.

Why is there any maximum fee?  Why not allow any fee?
How can you calculate the maximum fee acceptable without error?

That "Fee" is a different number when I try CPFP at different times of the day on this exact same transaction.  Sometimes it has been much higher, above 3 mBTC.  I can only guess that maybe Electrum is using current information it has pulled in from somewhere on the net about what threshold miners are currently accepting.

I can edit that "Fee" but I keep getting "Max fee exceeded" for what I think are reasonable numbers to try, between 2 and 3 mBTC.  My latest click came up with:

Total size: 416 bytes
Input amount: 1.2 mBTC
Output amount: -2.13808 mBTC <---- This has become a larger negative number for the exact same transaction
Fee: 3.3308 mBTC <------ This has become a larger number for the exact same transaction

There is a slide bar at the bottom, and if I move it, then it will quickly change the fee to 1.2 mBTC automatically, and moving the slide bar doesn't change this fee, it just stays at 1.2 mBTC whether it's slid all the way to the left, to the right, or in the middle.  No option, really.  If I click on OK on this 1.2 mBTC, then I can go to the next step without the "Max fee exceeded" error. With amounts higher than 1.2 mBTC manually typed it, it fails with "Max fee exceeded".  

However, recently, I have noticed that when it automatically switches to 1.2 mBTC, the "Output amount:" disappears, i.e., it is left blank.  This makes me afraid it may cause a problem later, but I haven't found any way to fix that.

Electrum has also crashed on me when I try to edit the Fee, multiple times.

Notably, this 1.2 mBTC seems to be a low fee for parent and child combined, i.e., averaging 0.65 mBTC in my case since the parent had 0.1 mBTC (not shown on this particular step screen) whereby (1.2+0.1)/2 = 0.65 mBTC.  I would like to set a higher fee to make sure the pair is mined and not get still another stuck transaction, but it won't allow me to.

* I fear that the automatic settings for Electrum, and the settings allowed, might create another stuck low fee transaction for the CPFP, and cannot be changed! *

Anyway, just for covering the final step, let's go past the step above to the next step below, so for testing I click on OK for 1.2 mBTC after touching the slider bar, so it doesn't give me the "Max fee exceeded" anymore, and goes to the next step.

At the top of the next screen is a field for "Transaction ID:" which has just the word "Unknown" and I can edit this.
At first, I wondered whether I supposed to put something into the field "Transaction ID:" or just leave it as "Unknown".
I found that if you click on the Sign button at the bottom, and then that field will be automatically added.
Then you click on Broadcast.

OK, I did that, but then I got an error message:
error: {'code': -1, 'message': 'the transaction was rejected by network rules.\n\64:dust
\n[a very long number in hex which exceeds the size of the pop-up box]'

Thus, I wonder whether or not Electrum is broken under current network conditions, or whether or not the current version of Electrum is just broken regardless of network conditions, the latest version 3.0.3

It's worth noting some other things, which would be good to understand.

On the last step (with the Broadcast button), the transaction says 625 sat/byte but that's only for the child, without saying it's only for the child. Since miners see both child and parent together, the actual total transaction would be seen as approximately half that in my case, around 312 sat/byte, which I think is still too low for miners these days.  My parent transaction was sent for just 0.1 mBTC mining fee (which will never go thru now) and it was of size 224 bytes so the total mining fee would be 1.2 + 0.1 = 1.3 mBTC and the most important thing for miners (as I understand it) is the sat/byte mining fee, which would be [ 1.3 mBTC / (192+224) bytes ] = 312.5 sat/byte , and likewise a fee of 0.65 mBTC per item for 1.3 mBTC together for 2 minings.  I would prefer it to be higher so it goes thru quicker, but I wasn't able to set it any higher, as noted above. Checking at the moment on December 31, it appeared to be able to probably go thru within 10 blocks or 3 hours.

Below that information are two fields which I cannot edit but which I am naturally curious about (and I have changed the numbers for privacy here), with the ones starting with 12AbWalletAddress34ABcd being shaded in green and are my wallet's bitcoin address:

Inputs (1)
2d848484...1a75ab75:1 [space] 12AbWalletAddress34cd5678efgh90ijklmn [space] 1.2

Outputs (1)
12AbWalletAddress34cd5678efgh90ijklmn [space] 0

I understand that the green shaded number is my bitcoin wallet address (which I have obviously changed in this example to be a fictitious one), but I have no idea what the first column is under Inputs (1) (also changed to a fictitious number but in the same format),
2d848484...1a75ab75:1

That's all I see for now.  If anybody can answer any of these questions, then maybe we can piece together this puzzle and come to understand how all this works, even if I cannot get my Electrum to successfully send a CPFP.

From what I've seen in my research, there is a very, very high number of stuck low fee transactions pending, so CPFP should be of use for many other people.  I also suspect that stuck transactions will remain common with bitcoin in the future, so demand for instructions like these might rise.  Already, the topics of low fees are extremely popular on this forum in terms of number of views.  I would like to try to help create a reliable and accurate guide for Electrum, the details that are being left out elsewhere on the web.  This would be a practical solution, step-by-step with real Electrum prompts which need answers, and explaining things to guide people. Either that, or we can point them towards an alternative with a better understanding.