Welcome to the forum proverb. I'm kind of new as well, but have been reading as much as I can over the past couple of weeks.

1. Once a block is found, the problem changes and your computer does have to change what it is looking for. This isn't a big deal because you have the same probability to hit a block so long as the difficulty remains the same.

2. Accepted is the response from a pool for a piece of the work (or share) your machine has done. You will see how many shares you have completed and this number is used to compute your payout when the pool hits a block.

3. Your miner will always need to check with the pool to get the latest work. There is no need to remember because your probability of hitting a block remains the same if difficulty remains the same.

Hope that helps.

SteveA