It's up to you whether to accept unconfirmed transactions or not. It is likely they'll be confirmed in short order, but there is still a possibility they might not, so for larger values you may want to wait for one or more confirmation(s)
Mining with your computer helps strengthen the Monero network. The more people mine, the harder it is for the network to be attacked, and every little bit helps. Mining also gives you a small chance to earn some Monero. Your computer will create hashes looking for block solutions. If you find a block, you will get the associated reward. Good luck!
