Are handbags and umbrellas allowed?

No they aren't

Clutch purse and see thru handbags. Not sure about umbrella

No. Leave them in your car. Wear a poncho if you're sitting outside the roof.

I had a small body bag, held phone, credit card, money, that's about all.

Small handbags (about the size of your hand) are allowed. Otherwise clear bags are needed.

I've seen people with clear bags