Is there a way to redeem a code as a gift so that I can still give it away but I don't have to hold onto this email and key (which I will most certainly lose after some amount of time)?

copy and paste it to a txt file ?

You can't store the key into your account if you already own the game, if that is what you mean.

Sort of. I know gifts given that haven't been taken yet are in your account and avail to give to someone else. I was hoping the same could be done some way with other GoG freebies.

Find a member you trust. PM him or her the code. Then it will be in your PMs here on the site, available to you whenever you log in. Or create an alt account (not sure you're really allowed to do this, however) and send a PM to that 'member'.

If, by any chance, you are thinking of the codes for the free Witcher 2 or the Gamers movie, be aware that both of these code expire on Dec 31, 2014.

Yes, you can store games on your account on certain conditions, here's an example, you can store as many free games like Warsow as you want. The key is to "purchase" it, the same goes for the insomnia sale-giveaway.