2. You don't necessarily need to download the entire blockchain if your computer doesn't have enough memory. Lookup pruned nodes, where you can only download like 15gb and such.
I am sure you already know that and it's just a miswording, so I want to clarify that even if you set up a pruned node, you will have to download the whole blockchain but only the most recent blocks (depending on your configuration) will be saved on your device. The minimum storage size you can set is 550Mb (
-prune=550).
I have lots of very old (2013) private keys generated on paper wallets from bitaddress.org with bitcoin on them. How do I go about importing them?
OP, if you are going to spend your Bitcoin or move it to a new wallet, don't forget to claim your fork coins. Here is a guide on how to do that safely:
LoyceV's Bitcoin Fork claiming guide (and service)