EVE New Citizens Q&A

No, you can't use your current non-buddy trial to get the buddy acct stuff.

It's about $20 to transfer a character.

Since you're only about a week in, I'd say trade all your stuff to your buddy (assuming he's a RL friend, and will give it back)... make new toon on the buddy acct, get 3 week trial and say "meh" about the week's worth of training you have to re-do.

Two weeks worth of training and missions isn't really that much in the grand scheme of things. On the other hand, you might be able to get somewhere with a petition, assuming your friend had sent you a Buddy Invite but you created a 14 day trial instead. On the gripping hand, if you can remember any of the details of that old 200X account, you might be able to reactivate it. How long had you played that old account for? Would it be worth recovering it?

As for missions and standings, you'll find that your personal experience in playing the game will give you just as much benefit as a few days worth of SP.

Don't fret too much: you've had fun, you've learned a bit about the mechanics of the game, and by starting a Buddy invite trial you'll effectively get more game time for free :) On subscription, the Buddy Invitee gets the Cerebral Accelerator, so you'll be in even better shape by the time the trial period is over. So subscribe earlier rather than later to get the most out of that benefit.

Update: the Cerebral Accelerator provides +3 to all attributes (effectively speeding up your training time without having to train Cybernetics), and grants 1/5 improvement to DPS, until your character is 35 days old.

It's worth restarting with the Buddy Invite (and subscribing immediately) just to get the Cerebral Accelerator. You'll keep the 21 free days of the Buddy Invite trial period, which will be supplemented by whatever period you subscribe for.