You can have a segwit wallet with electrum, if you have the latest version.

• New/Restore
• Name your wallet and click Next
• Create a new seed

Segwit is by default selected as you can see:


If you continue electrum will derive you Bech32 addresses (starting with bc1) and not p2sh (starting with 3). In order to derive p2sh addresses you'll need to enter your mnemonic on "I already have a seed" --> (leave it blank if you don't want a passphrase) --> choose p2sh-segwit.

On the same wallet? Yes.
In order to have different type of addresses on electrum you'll have to

• Create New/Restore
• Import Bitcoin addresses or private keys

Enter these before the private keys for whatever address type you want:
p2pkh: (starting with 1)
p2wpkh-p2sh:(starting with 3)
p2wpkh: (starting with bc1)