I have no objection, clearly, to you participating in the questioning of witnesses. That is the practice on all committees I have sat on, whether it's been a subcommittee or a committee of the whole. The chair has, from time to time, sometimes very regularly, sometimes sporadically or very exceptionally, reserved some time to ask questions and clarify issues. So I have no problem.
I would suggest that if we're allotting time, because that's part of our rules--the first round is x amount of time, and so on--that we empower the clerk to keep an eye on the timer and signal when our time is up, the same way you do with the members here.
In terms of voting, normally the chair does not vote, and unless the clerk tells me that on subcommittees of Procedure and House Affairs the tradition has been that the chair has voted, then I'm not interested in having the chair vote.