Can I Replace An Old Wallet.dat File In Bitcoin Core Before It Fully Syncs?

I have an older wallet.dat file I'm trying to re-open in the latest Bitcoin Core version (0.20.1). Once I replace the empty wallet.dat file with the older one:

1. Do I need to wait for the entire blockchain to sync before seeing the contents of the wallet? (The point I'm at in downloading the blockchain is well past where the original wallet date was)

2. If I'm able to see the entire contents of the old wallet before the blockchain is finished syncing can it be done offline or do I need to keep Bitcoin Core online?

I assume you are cleanly shutting down bitcoin-core before you overwrite wallet.dat. This is absolutely a requirement. You can't replace an open wallet file while bitcoin core is running.

#1 - Yes, you need to complete the initial block download to see the contents. Since you already download some blocks before the wallet born-on date, you will need to issue a rescan to look for wallet transactions before the block your currently downloading

#2 - You can always see the keys of the wallet regardless of how far the download has gotten, but you won't get the balance until the download is complete. Once you have all the blocks you can do everything offline, but of course it won't see TXNs in blocks that you haven't grabbed since going offline.