I never did that but I'm sure you can. What you can't withdraw without "playing" first is bonus money from any promotion they might have, but I'm sure you can withdraw the money you just deposited. (the only "restriction" like I said before is that you must use the same method you previous used to deposit. If you deposit let's say $30 with neteller you must withdraw them from neteller and not by any other method)
This is wrong. Betfair and most other sites require you to make at least a bet (or multiple bets) with the size of the deposit. Some bookmakers even require you to turnover your deposit
multiple times (pinnaclesports.com).
The reason for this is the deposit fees that Betfair has to pay to the e-wallet providers like Neteller and Skrill.
If you would deposit and withdraw without playing they would make a guaranteed loss due to the above mentioned fees.