No, you do not. You can open an account by post, email or phone. You might need to send proof of identity though.
You can opt for a private banking service and get your own banker to perform transactions, yet most people handle transactions themselves.
It depends on the currency you choose – they may take anywhere between less than a second and a few minutes.
All digital currencies evolve and fluctuate. Some of them are better than others in terms of longterm productivity, but it is up to each user to choose what they are interested in.