Snape isn't really a true death eater he betrayed them and became a spy for the order.

Umbridge was working for the death eaters indirectly when the death eaters took over the ministry.

Umbridge is also not a death eater, she just works for them. And I guess she can produce patronus because she may have happy feelings from tormenting or annoying people.

She is not exactly a death eater tho, like @Ellie Romanoff of Winterfell said she just worked for them, but in cursed child she became a death eater when voldemort won hogwarts battle, so she's just probably on the strongest side.

No, she's not....and any accomplished wizard or witch can produce one eventually...I would also like to add a quote from Sirius. When he was talking with the trio about Umbridge through the fireplace, he said : -

"The world isn't split into good people and death eaters."

So there you go.....it's not necessary that she is a death eater..