Creating a wallet using a public key will generate a watching wallet. Basically, it means you can see the deposits and withdrawals, but you can't make any withstands.

To withdraw or "spend" coins you must have a private key. So if you export your private key and import it you will definitely be able to spend any coins in that address.

As for the backup, by default, Electrum will generate what is called a "Hierarchically Deterministic" or HD wallet. This is just a fancy way of saying that given a set starting point, it can regenerate the same addresses/keys all the time. As opposed to  older wallets like MB Classic that just regenerates random addresses.

The set starting point is known as the "seed" or "wallet words". This means you just need to write down your seed and keep it somewhere safe and you'll be able to restore your whole wallet just using the seed.

Because HD wallets generate a set list of addresses/keys, generally,  you cannot import private keys. You need to "sweep" the key which effectively creates a transaction that sends from your old address to an address in your new wallet.

Electrum will allow you to create an "old style" private key only wallet that you can import into, but then you won't have a seed to be able to backup your wallet with. You'll need to make backups of your wallet file (and/or the keys)...

So, the best plan is create an HD wallet and then sweep the private key(s)... You'll have the security of a seed based wallet.