1.) Storage of database passwords Use some kind of hash with a salt and then alter the hash, obfuscate it, for example add a distinct value for each byte. That way your passwords a super secured against dictionary attacks and rainbow tables.
2.) To check if the password matches, create your hash for the password the user put in. Then perform a query against the database for the username and just check if the two password hashes are identical. If they are, give the user an authentication token.
The query should then look like this:
select hashedPassword from users where username=?
Then compare the password to the input.
Further questions?