No, I mine on my own node.  Of my miners, I have some with difficulty set to /256, some at /512 and some not set at all.  I have seen absolutely zero impact from setting them or not.

Oh good... another shill account promoting the wonders of pbmining.  Here's something for you to consider: PBMining is a nothing more than a Ponzi scheme.  They have not proven they actually mine anything at all.  Payouts are exactly "expected" earnings.  Payouts are sent through mixing services.

Site - None.
My GH/s - 4TH/s of hardware that I actually own
Pros - There are no pros to cloud mining, unless you're the guy providing the cloud mining service, in which case there are plenty.
Cons - Most are scams with no proven mining actually happening.  All are overpriced and will never get you ROI.  Many have hidden fees in their structure (example, maintenance charges).

Seriously.  Save yourself the trouble.  Do NOT become a cloud mining consumer.  If you want to mine, purchase the hardware.  You can have it hosted, if you can't have it at your home/dorm/apartment/whatever.  There are a number of vendors who provide co-location services.  Not all of them are overpriced.

1) It's the statistical mean of your expected payout over the plotted range of the graph
2) Depends on what you mean by "good".
3) Use a different UI

Use a different UI - there are plenty of them out there, and they usually all will provide you more information than the stock one does.

You definitely want to find a node that is close by, but keep in mind that you want that node to be stable and efficient.  For example, it doesn't make a difference if you've got a node 10ms from you if that node gets 95% orphans and DOA.  Look at a node's efficiency rating to see how it's doing.  Anything over 95% is good.

That's using stock queue settings (--queue 4096).  Like I said... most stable one I've got - set it and forget it.  Best share is 0 because of what I reported earlier - manually setting share difficulty.

Hopping from p2pool node to p2pool node is perfectly fine.  This is because the share chain is shared amongst all nodes that make up p2pool.  You don't lose anything at all.  What I was mentioning earlier was hopping from pool to pool.  In other words, from Eligius to p2pool to Slush, to BTCGuild, back to Eligius, etc.  That is a bad idea.  However, hopping from my node, to windpath's node, to norgz node, back to my own node is no problem at all.  Everything carries with you because the share chain on my node, on windpath's on norgz is the same.

I'm noticing that as well on my "lucky" one.  Very low HW errors, low rejects, stable hashing at 504, temps at 40... it is the closest to "set and forget" I've found with the S3s.  All of my others... constantly babysitting.

Yup, the mysterious "x" that randomly will show up, drop your hash rate by 15GH/s or so and disappears.  Changing miner configuration from the UI, but the mining process never actually starts.  Clocking 1 unit at 218.75, another at 212.5, another at 225, to find the most stable speed.  Some units with unbelievably low HW errors, others with high rates.  Some with high rejects, some with low.

I've ordered from batch 1, batch 4 and batch 5.  Even in batch 5 the issues remain, although I did get "lucky" as one of my batch 5 units actually hashes at 504GH/s stable.
Yet another example of differences in things.  I've never noticed any hash rate difference on my units by setting queue to 0, 1 or stock at 4096.

ckolivas recommended to use at least queue 1 and not queue 0.  Also, I just use the default failover option (since my backup pools are p2pool nodes, it really doesn't matter on which one I'm mining).

I've tried virtually every incarnation of settings on my S3s: queue, expiry, scan-time, manual share diff, manual pseudo-diff, etc.  I have detected absolutely zero difference in performance.  As I mentioned many pages ago in this thread, the only thing I've ever seen is that the value of "Best Share" is always "0" when I set my miner to use /#+#.

YMMV though.  One thing I have noticed is that the S3 is finicky.  Right when you think it's good to go and stable, something else pops up.  Just because I noticed no difference, somebody else might.

Answer to your first question is yes.  The pool only pays the previous 8640 shares.  That's the way PPLNS payout systems work - N in p2pool's case happens to be 8640.  If you don't have a share in that set, then you don't get any coin.

If you're trying to predict luck... well... good luck with that.  It's called luck precisely because it is unpredictable.  You cannot state that something's been lucky, so therefore it must now become unlucky.  That's a fallacy.

Anyway, more on topic of the underlying question you asked in that paragraph: any PPLNS system discourages you from pool hopping.  For example, you should mine on p2pool for at least 3 days to get a good distribution of your shares on the chain.  Mining there for a few hours is pointless.  If you want to hop around from pool to pool, PPS pools are your friend.

The 0.5% is awarded to the miner who found the block, not the node on which they were mining.

Pretty much summed it up.  0.5% goes to the guy who found the block, the remaining 99.5% goes to everyone else.

I'm not sure what you're implying here.  If you stop your miners, you still get payouts until your final share falls off the chain.  Obviously if you've stopped mining, you don't have any hash rate.

So I've been following this experiment since you started.  Let's examine what you've done vs the other guy.
1) You setup a rig virtually identical in hashing power to his to keep things equal on that level
2) You set your rig to only submit shares that would solve a block, whereas his rig was set to difficulty defined by the node.
3) The difficulty you set is approximately 1000 times higher than what he has.

Over time, both of your payouts will even out.  Each of your rigs will take approximately the same time to find a block, and each has an equal chance of doing so.  The difference is that while he continues to submit shares to the chain, you do not until you find a block.  This means he'll have 1000 shares to your 1, give or take.  However, your 1 share will be worth about 1000 times what his is.  When the block is found, and the payouts are generated, all of the shares on the chain are weighted to determine how much of the 99.5% of the block reward each share gets.  The XJO chain is 4320 shares for payout, and the reward is 16 coins spread over those shares.

Since he's just as likely as you to find the block, the "finder's reward" will be split evenly between the two of you.  This leaves us the shares on the chain.  As I stated in the previous paragraph, he'll have far more shares on the chain, but each will be worth about 1000th of yours.  Upon payout, you're going to get about the same coins.  Yes, there will be times where you find a bunch of blocks and have more shares on the chain than you should.  There will also be times when you have no shares on the chain because he's been finding the blocks, and you haven't found any.

In conclusion, your experiment simply has not run long enough to provide proof of your claim.  If you were to let it run, you'd see it play out as I have stated.

Yup, that's the one that will connect you to the Elizium p2pool node.

Yeah Josh offers a really decent package but what he offers is more akin to co-location than cloud mining.  You actually purchase and own the rigs.

Normal network variance swings.  Sure, there is always some new hardware being added, but think about what you're saying.  4000+ SP30s added in the past few days?

Shares are not worth a static value.  Each share is given a weight when you find it.  When the block is found, you're paid for that share's weight.  That's why if you look at some of the front ends (like mine, windpath's, etc) you'll see your expected payout constantly changing because your shares' weights are constantly being evaluated and calculated should a block be found right then.

For your second question, that's subjective.  It's the way it works.  To be paid, you need shares.  Your mining rigs are constantly working and submitting work to the node.  The node evaluates that work and determines whether or not it satisfies the difficulty to become a share on the chain.  If it does not, it is ignored.  If it does, a share is added to the chain and broadcast to the rest of the p2pool network.  So, just because you didn't find a share doesn't mean you're wasting work.  It just means you haven't yet found one that would be added to the chain.

What does this even mean?  P2pool payouts are exactly as I described them above.  When p2pool finds a block 8640 shares are paid as part of the generation transaction.  If you want to be paid you need to have at least 1 share on the chain.

Let me out it another way.  Each time you find a valid share that gets added to the chain, you are paid for that share every time the pool finds a block until such time that that share falls off the chain.  This is approximately 3 days.  So, if you just started on p2pool yesterday and found a share before 18:30 EDT, you would have been paid 6 times since then because p2pool has found 6 blocks.

You don't get anything.  To get paid on p2pool you must have a share on the chain when a block is found.