In general, ‘Working’ is a little more complicated or difficult than ‘doing’. The week in Hawaii did wonders for my morale! I haven’t been this happy in a long time. (It’s obvious that good weather and vacation can make people feel better) He’s had trouble losing weight but his intermittent fasting regime is working wonders. (Sticking to a detailed plan requires some work)

I would say they mean roughly the same, but the subject of "do wonders" - almost always followed by "for..." - normally is not human, whereas the subject of "work wonders", not normally followed by "for", is normally a person or group of people. My gardener has worked wonders in my garden. The theatre company have (/has) worked wonders in bringing this to the stage. Try this face cream, it'll do wonders for your complexion. He used to have an anger problem, but I told him to bite his tongue and count to 3000, and it's done wonders for him. Having said that, you can use them interchangeably to a great extent. I think if you're unsure, use "work wonders".

Both mean the same. Grammatically ‘do wonders’ is usually used in the past tense. I took my medication for a month and it did/worked wonders for me. Take this medication for the next month, it should work wonders for you.