Is it possible for non-Mileage Plus customers to buy into economy plus at check in?

Yes - several times when I have flown US they give me this option at kiosk check-in. Once it was a reasonable deal. Other times they tried to sell me a middle EPlus seat instead of my aisle economy seat.

Yes, but only if there are any economy plus seats available. You can also buy economy plus access for yourself and a companion for $349 per year.

If you buy econ+ yourself as Jack mentioned, you can select the seats of your choice when you make your reservation rather than take whats left during checkin.

I don't have much personal experience with when and how often the buy-ups are offered because I'm eligible on status, but apparently they're also offered on occasion at purchase (as opposed to check-in). I recently booked a ticket for my husband via the United website and received an offer--I think somewhere around $35 each way for Chicago-San Antonio-Chicago flights.