I have read the following links and have a question similar to them:

All we seem to do is argue or is arguing

“All you have to do is read” vs. “All you have to do is to read”

"What I have to do is" + verb inf

What form of verb should expressions like "All I want to do is" be followed by?

Based on these links, I suppose the sentence:

1. "All I do lately is listen to music".

is right, and the sentence:

2. All I do lately is listening to music.

is wrong.

But what about these:

3. "All I am doing lately is listen to music".

4. "All I am doing lately is listening to music".

Does the present continuous form of the verb ("doing") makes the phrase coming after "is" to be a gerund?

Maybe the original form of this sentence is

5. "All I am doing lately is [I am] listening to music".

Where [I am] is omitted so it is reasonable that the present continuous form of the verb ("doing") propagates to the phrase after "is".

What ever the answer is, can I generalize the answer to all the following expressions?

6. What I am doing lately is study/studying.
7. The work that I am doing lately is draw/drawing a picture.
8. The dream that I am thinking about is go/going to a trip.