-Can I convert the wallet.dat file to a modern wallet file, preferably for a lightweight wallet like electrum?
No, the best you could do is dump the privkeys and import or sweep them into another wallet.
-Will the newest official bitcoin wallet work read the old wallet.dat file?
Yes, but you'll need the blockchain fully downloaded and sync'd to be able to spend the coins from the wallet.
-Can I import the JSON file into some sort of modern wallet file?
Probably not.
-Can I do any of these steps on an offline computer to ensure that if I make a screwup I can just start over?
Yes... and it goes without saying that you should also use COPIES of the wallet files... do NOT work on the original files.
Another concern I have is retaining access to the bitcoin cash version of these bitcoin as well as both versions from the upcoming fork.
-Will I loose access to bitcoin cash and the new forks depending on how I try to recover these old bitcoin files?
No, you will NOT lose access to BCH, as long as you have the original wallets and/or access to the original private keys... you'll be fine.
Best of luck with your BTC recover, seems like you've got quite a happy little stash if your "smallest" balance is ~2BTC!