I fly into Seattle at 10:35am and my flight to Seoul leaves at 11:15am. Will I have enough time to get to my connecting flight and do I go thru customs at that point?

Doubt it. Seatac staff will find a way to mess it up

You maybe right on time or pushing it depending on how far apart the arrival gate is from the departure gate. You go thru customs when you arrive in Seoul

I RECOMMEND TO GO IN 2 HOURS AHEAD OF TIME ESPECIALLY THIS WEEKEND IT WILL BE PACK. YES ID AND PASSPORT HANDY. SECURITY IS A HASSLE IT TOOK US AWHILE TO PASS THROUGH. LESS THINGS TAKING WITH YOU AS PERSONAL BAG OR CARRY ON THE BETTER.

I don't know if you have to go through customs as I have never traveled internationally. However, I did hear announcements being made for proof of vaccinations and covid tests. As for enough time to catch the next flight, it depends on what you have to do to catch the next flight. I don't know the procedures. You might be already cleared for everything and just need to walk the distance to catch the next flight. You must have your ID ready and probably your passport, plus ticket.