I haven't put much thought in replace by fee yet, but I tend to doubt it. It seems an incentive to attempt double spending (although I do understand Peter Todd's explanation on how to take measures against this, as a merchant getting ripped off from double spending).

Yeah, BitUndo pretends do be a nice service to the Bitcoin community of some sorts, but imho it's actually very bad that this exists.

But if I'm no mistaken, BitUnfo still does distributed mining, since essentially it's "just another mining pool" (except with specific purposes and rules) right? How do they keep the transactions secret? Do they deliberately not relay any transactions until mined, or...?

I'm trying to setup a way of accepting Bitcoin payments in real life situations, where waiting for confirmations is typically not an option. I understand this is never 100% risk free (especially with crap like bitundo.com around), I just want to minimize the risk.

I've got a Bitcoin Core wallet with a bunch of unused addresses. I show the customer an address, he sends the money, and now I can do a few things: (all automated, i.e. through some kind of application or script)

1. Check if the (unconfirmed) transaction appears on my own node / in my wallet
2. Check if the (unconfirmed) transaction appears on sites using online APIs like blockr.io and blockchain.info
3. Check if I don't see a similar transaction (from the same input address, but to another output address, i.e. a double spend attempt) on either my node or API sites.

If 1 or 2 are OK and 3 doesn't occur for e.g. five to ten seconds, how (un)certain is the transaction at this point?

I noticed that payment providers like bitpay and coinbase can sort of accept payments immediately, how do they tell legit transactions from double spend attempts?