How do you know if your partner is actually sending you gifts? I have sent a few to mine, but I haven't gotten any sort of notification that they've been returning the favor..

Which means that they haven't sent anything back. You usually get an event.

that's what I was afraid of... OH WELL! It's not a big deal, I didn't give away anything i'd miss too much... I personally believe there should be a 1 gift minimum requirement.. :(

It's possible they logged off before they were matched up with you. That almost happened to me the other day. I entered my name but I didn't have a partner right away. By the time I was paired up with someone, I was almost ready to shut down my computer. Luckily, I was able to send off a couple gifts quickly before logging out.