~When I start electrum it doesn't ask for a password, it immediately opens giving access to my wallet. I don't understand why is this happening, every tutorial I've read says that the password is needed every time you open electrum. What am I missing?
what is the version of the Electrum installed on Tails?
a couple of versions before, Electrum password worked differently. by default you could open your wallet, see the transactions, balance, addresses,.... but to access the keys (seed, private key, signing, ...) you needed to enter the password.
they changed this behavior and now when you choose a password you have to choose what to encrypt. it can be the old behavior or encrypt everything.
you are either running an old version or didn't encrypt everything.
p.s. i think it was changed in 2.8.0
Another question I have is regarding other cryptocurrency wallets. Will Tails allow me to install other wallets using persistance?
if you add persistence then yes. but it will be a big complicated.