First of all, addresses starting with a 3 do not necessarily have private keys associated with them, and not necessarily 2 or 3 private keys. Addresses starting with a 3 are P2SH addresses which means they have a script associated with them, and that script can be whatever you want so long as it is a valid script. This means that it can contain many public keys (and thus have many private keys) or no public keys (and thus be associated with no private keys).
bech32 addresses are for the P2WPKH and P2WSH output types. For P2WPKH, there is one private key. P2WSH is like P2SH; it is associated with an arbitrary script.
Also, there are no types of private keys. All private keys are the same "type"': a 256 bit integer.
Bech32 addresses have built in error detection and correction (they can correct, but software should not be automatically correcting errors). I don't think they are any more or less secure than "normal" addresses.