Sony really came out of nowhere with that stuff, and it's still a mess for me, but you def don't need a phone of any kind, as long as you have access to the internet (And your email address)
I have 2 Sony accounts, and i couldn't recall the passwords for either. Password reset has stopped working since this all began, so I'm still locked out of my second account (I remembered my main account password). My brother has been locked out of his Vita too, since he can't recover/change the password. Since it's only a secondary account I haven't bothered, but if you really want to get access again you are likely going to have to contact Sony.
You can technically play physical games without your account, but previous saves are associated with the account (Maybe all, IDK).
if you do sell off your stuff, you would get more selling individually. If you have something cool like a complete Vita collection maybe consider going through an auction house.