The matter is one of grammar. In the context you are talking about, do is acting as an auxiliary in the have does. The problem is the use of a double auxiliary. This can happen with the tense and voice auxiliaries, have and be, but not with ‘do’.
Even here there is an exception. Somerset dialect, now sadly moribund, permits
“I do go to the gym every ...
Square brackets are used for interpolations and clarifications from the author and can enclose arbitrary meta-text (though this normally kept short). Examples are:
negative press covfefe [sic]
she wrote "you shall go to the ball" [my emphasis]
she wrote "you shall go to the ball" [author's italics]
The earth is round [editor's note: corrected from previous ...
No, it depends on your intent.
You could say “I can do football”, with a literal meaning being that you are capable of football and an implied, more colloquial meaning that you are capable of (joining) football.
I don’t know if there is a deeper, more exact rule, but as a native English speaker that’s how you’d sentences akin to this one.