Why do you want to use pywallet as first step?

To your first question: how can someone give you an answer if you don't say what OS was used?

For Windows if copied with File Explorer across different volumes:

• the modification time stays the same as the source file
• the creation time of the new file is the current time (not displayed by default)

To your second question: pywallet is a known tool if you download it from its known and reputed sources. But again, why pywallet as first step before you tried to open your wallet files in Bitcoin Core?

Make multiple backup copies of your wallet files, so that you can't ever loose the original files. You only work on copies of copies. Document any step, so you don't loose track or confuse yourself.

What is your prefered OS?

This is what I would do if I don't have Bitcoin Core. Open Bitcoin Core and set it up as a pruned node, the amount for the blockchain doesn't need to be large, you can stick to the default of 5 or 20GB (forgot what the default is, my nodes aren't pruned). When it start to sync, take your device offline to interrupt blockchain download temporarily.

Now load all your wallet files into your Bitcoin Core node. When all wallet files are loaded, you can proceed with syncing the blockchain. This can take a while to finish, maybe a few days. If you need to interrupt the sync process make sure to always shutdown Bitcoin Core cleanly!

When the blockchain sync has finished, see if you have coins in your wallets. You can switch from wallet to wallet by selecting the wallet with the dropdown menu in the upper right corner of the Core window.