That's the thing, I'm pretty sure check clearinghouses are near real-time these days. At least in the US. Deposit the check and within a few minutes it'll either clear from the other bank or bounce.
Nope, it's still a batch process. Usually the day's batch is collected and sent to the Fed, and then the bank gets their net debit/credit for all their transactions. It'll generally show in accounts the next morning. (Note that there are many details here about exactly which method is used and if there's a third party exchange).
Checks can come back anywhere from nearly instantly (e.x if there's a bad routing number) to a day or two (insufficient funds, or bad accounts, or unauthorized on a commercial account) to a month or two (unauthorized on a personal account) to many months (fraud, US treasury checks). The last can be a real killer, since they're normally big checks on trustworthy accounts (though, not necessarily from trustworthy intermediates).
Checks are never really cleared, they just haven't bounced yet.
Unless it's a large check, in which case it's normal practice for a bank to put a hold on all but a small portion of the funds for several days. The exception is for deposits which occur regularly from the same source, like payroll.