Have there been made any calculations how high the transaction fees for bitcoin main network could get in the future?
The only thing more impossible to predict than the price of Bitcoin in the future is the price of Bitcoin's fees.
I currently have my BTC stored on a MultiSig cold wallet, which can't be connected to a lightning node. Do you think it's a better idea to move them to a lightning wallet like on electrum for example before the transaction fees get too high? I want to avoid paying a big amount just for one transaction in the main network
If you are storing your coins for long term, keep them in multisig (and make sure you don't accumulate too many small UTXOs). If you are spending your coins, keep some in Lightning.