Is it possible to know when I will get newly minted bitcoins from my processing? I've been generating for a few weeks now and haven't seen any. Does everyone get new bitcoins at once?
You can't know when. It's normal that you don't see any, current difficulty is really high.
This site calculates some probabilities: http://www.alloscomp.com/bitcoin/calculator.php
I have read about backing up your wallet.dat file but not much about restoring from backups - do you simply install Bitcoin and then write over the wallet.dat with your archived version of wallet.dat?
Yes, it should work.
If you archive your wallet.dat and then a make a transaction, and say your hard drive crashes and you restore your old wallet.dat from before the last transaction - does this restore everything you had before that transaction? And the last transaction after backing up is then lost forever?
No, you risk losing money in the process, due to the change process.
The best is to back up always after any of these events:
- Sending any amount
- Creating an address for receiving
- Generating something (not really sure about this one though)
I've seen some messages on the forum that a pool of addresses is under development. After it's implemented, you won't need to back up so frequently.
Say I reinstall my OS and then reinstall Bitcoin and recover with my old wallet.dat - do I keep my progress I had made minting my next bitcoins, or do I have to start over from the beginning?
It's not a progress. Each hash you generate is a random attempt, each of them has the same chance of breaking the last hash.
Think of it as a lottery, each hash being a ticket.