I don't understand why your older version would work and mine won't.
His wallet file from the old version does still work. But he isn't using the old electrum version.
There is backwards compatibility. You can upgrade electrum and still use your current wallet file.
[...] at the bottom left where it used to say the balance it now says synchronizing... and it doesn't seem to synchronize.
Yes, because you need to upgrade electrum.
I believe you always have the option to export a private key. Just make sure your computer is secure and preferably offline.
Save the private key in a safe place and import it into a new wallet.
There is no reason to do so.
1) If his computer would be compromised, his private keys are compromised already since the wallet is running on this computer. Whether he exports the private keys or not, does not matter.
2) He can always - if his wallet file won't work in the newer version, which won't be the case - just use the older version of electrum again to access his keys.
Your suggestion is by any means worthless.
Are you saying to go offline then export the key (which I have on paper but will do digitally too). Then upgrade the Mac OS first so I can download the new version of Electrum. And when that is done I should be able to import the key and the wallet should work?
No. Don't listen to him, he doesn't know what he is talking about.
First, the fact that you don't have your mnemonic code is extremely bad. You shouldn't use a wallet of which you don't have a non-digital backup.
Get the mnemonic code by going to Wallet -> Seed. If that doesn't work, create a new wallet and move your funds to your new wallet. This can be done after upgrading electrum.
Second, create multiple copies of your wallet file and do not only store them on your PC. After you have done that, upgrade your OS and electrum. Then open the backed up wallet file.
After that is done, create a new wallet and
write down the mnemonic code. Send all your funds to that new wallet.