Of course you can open a checking account without direct deposit. You just physically bring in your deposits. My income is in the form of checks and direct deposit is not an option, but I had no problem opening a checking account.

yes, but depending on teh bank, nowadays a lot of banks will charge you a monthly fee unless you have something setup with them, such as direct deposit (terms vary per banks)

yes - you don;t even need a job - you just need money

No