Quote from: Spangles on January 16, 2018, 10:27:18 AM

Is it possible to move my wallet.dat directly to a hardware wallet such as Tresor? I am using Bitcoin Core and want to move my wallet off my PC to more secure storage.

Thats completely against the purpose of a hardware wallet.
Once your private keys were on an device connected to the internet (your current pc), those should be considered as possibly compromised.
The only way to guarantee a safe storage is to let the private keys be generated by your hardware wallet (which will never leave the device) and send your funds over.

Quote from: Spangles on January 16, 2018, 10:27:18 AM

Also, it is possible to access my wallet in Bitcoin Core without downloading the whole blockchain. My client crashed recently with a message that said "Error: a fatal internal error occurred, see debug for details" .

Not directly.
You can export the private keys / the master private key (starting with xprv..) and import them into another wallet (e.g. electrum: https://electrum.org/#home).
To export your master private key in core. Go to 'Help' -> 'Debug Window' -> 'Console'.
Then type in walletpassphrase YOUR_PASSWORD to unlock your wallet and dumpwallet FILE_NAME to dump your allet into a file.
Afterwards you can open this file with an editor and serach for 'xprv'. This master private key can be then imported into any BIP44-compatible wallet.