-snip-
Yeah, I know. They have a shady past and development is near zero. It was the first thing on hand and it did the job.
Feel free to suggest other multi-coin desktop wallets with a built-in exchange. I think none are open source and really trustworthy?
I don't believe there are any. If you're willing to switch to a mobile wallet, then you have Unstoppable wallet. It has a swap feature but you can't use it with BTC, LTC, etc. It uses Uniswap (ETH), QuickSwap (MATIC), PancakeSwap (BSC), and 1Inch which is an aggregator.
Or he can get an hardware wallet that support multiple coins.
This is incorrect, electrum does not store your private keys, it is stored on your wallet file locally (on your device) and encrypted with your password.
Can can be able to get your private keys directly on Android Electrum versions below 4.4.0, but this has been removed from version 4.4.0 and above.
On desktop Electrum, if you click on wallets -> private keys -> export. You will be able to see your addresses and the corresponding private keys. Or if you click on view -> check addresses. Click on addresses on the GUI and right click on any address of your choice, you will see the address private key if you click on 'private key'.
What is most important is the seed phrase, because it can generate all the addresses.