That's why there is an old adage here, BYOB (Be Your Own Bank). However, there are coins that are centralised, so I don't know if you consider it as having full and total control of your funds. It's also up to you where you store your crypto, if you put most of it a centralised exchange, then you forfeit the control as those exchanges can be hack or they can selectively scam you and will ask for your personal info, i.e KYC.

Yes, crypto is bonder less, you can be on the other part of the globe and send some on the other side. And the speed of the transaction will depend on how much fees are you willing to make, if you are in a hurry then you might want to increased your fees.