To do and to be never* (see below) mix in the same clause / sentence. Either of them is enough, depending on the context.
Your examples will be OK like this:
a) Is the feature still available?
b) Are the markets open?
If your question must use to be, then to do is no longer needed.
However, if your sentence does not have / does not need to be, then to do is needed:
Do you have some time?
Did you go to the concert?
Additionally,never mix to do with the modal verbs: can / may / must:
Do you can sing?
Can you sing?>
Do I may wait here?
May I wait here?
To form an interrogation with must, then you need to use to have to, and therefore use to do:
Do I must pay?
Do I have to pay?
(*) One exception when "to do" and "to be" fit together in a sentence is when "to do" has the purpose to emphasize the action (in this case, "to be").
As @phoog so cleverly provided an example in the comment:
Do be careful not to mislead anyone.