1) Buy your Oyster card when you arrive, no advantage in buying ahead of time (and may cost you postage as well).
2) You will need two cards, one each. The cards are not personal, you can lend them to other people, but two people cannot use the same card at the same time.
For the tube you "tap in" and "tap out", this opens the ticket barrier, and calculates your fare which is based on the number of zones you go through.
For buses you just tap in, the reader is by the driver. Fares are "per trip", so no need to tap out.
With practice you can use the card and walk through the ticket barrier without having to slow down, just like a real Londoner. Never, never wait until you get to the ticket barrier / get on the bus before searching for your card. That is a good way to annoy the people behind you.
The card reader has a small display which shows the amount left on the card. It only appears for 1-2 seconds, you have to be looking at it. You can refill the card at many shops as well as all tube stations.