Do coins stake while in the web wallet or do they need to be moved to desktop wallet?
Coins do not stake inside the webwallet. Because we allow partial withdraw in the wallet, the address your funds are actually in changes over time.
We'll have a staking pool in the future to bypass this. You can than deposit to a special generated address, and your funds will stake on that address. On withdraw, your whole balance is getting withdrawn at once from that specific address straight into your webwallet.
Do coins stake while in the web wallet or do they need to be moved to desktop wallet?
You can let your MAR in the web wallet. No need of the desktop.
Yes. funds can stay in your online MAR wallet at all times.