Should I buy an hardware wallet in order to diversify risk or paper wallet is enough ?
Electrum (if it's used properly) would be secure and you won't need a hardware wallet. Take note that if you want to be completely secure, you should run electrum on an air-gapped device. Otherwise, your wallet would be always prone to hacking. If you can't have an air-gapped device for any reason, it would be better to go for a hardware wallet.
Also note that you won't have a secure wallet just with generating a private key and address and printing it on a paper.
A paper wallet is secure, only if it's generated using the correct method. This means that it should be generated using a safe tool on a safe device.
I also recommend you to work with a HD wallet with a seed phrase. In this way, you can have numerous addresses all generated by a seed phrase. You can write down your seed phrase easily on a paper while there's a big possibility that you make a mistake when writing a private key.
Do splitting 1/3, 1/3, 1/3 of bitcoin in 3 different wallet/private key would eventually diminish risk instead of only one wallet ?
You can do that. But a single wallet would be enough if that have been generated in the correct way.
Again, you only need to keep your seed phrase. You won't need to keep individual private keys.
What about multisig ? Running my own node ? Useless in my case ?
All depend on your needs.
If you want to generate a wallet, send some bitcoin to that and just hold them, you won't need to run your own node.
With using a multi-signature wallet, you would need multiple seed phrases for accessing your fund and in this way, you may increase your security.
Use a multi-signature wallet, only if you know what exactly you are doing.