I backed up my private keys. Can I use these private keys in other wallets too? Let's just say I've backed up the seed words of your wallet. What if the electrum project is canceled in the future?
If you are talking about the private keys being exported, then you can. Even if Electrum goes down, you can still create your own server and send your coins elsewhere.
By looking at Bitcoin's address, can we tell which wallet was created? Every wallet seems to be creating a unique address for itself. But money can be transferred between different wallets.
For example, I backed up private keys in the electrum wallet. Can I use the addresses in the electrum in a different wallet using these private keys?
No. Addresses cannot be tied to the client which generates it, if the client does not have any bugs.
Yes. It's a different story for master private keys however. Not all wallet will support them.
For example, I backed up the private keys of my addresses in the electrum wallet. How can I install multibit hd wallet from again using these private keys?