Of course a test chair who is an active skater should be able to test on test sessions she has organized.
Where else is she supposed to test if not at her club's own test sessions? Depending where the club is located, she might have to travel more than a day's drive to find a test session she didn't organize. Or should she give up her organizing duties for the whole session every time she wants to test? Who will take over?
I don't think someone should judge and test at the same session, but really, I'm not sure why I think that. They wouldn't be judging themselves afterall, and tests aren't judged against how other people did, so it doesn't really matter if they judged that morning.
I have done this. In fact, every time I have tested since I became a judge.
My club has full-day test sessions, and I live walking distance from one of the rinks where we hold test sessions. So I plan to test at that rink, test in the morning, go home to shower and change, and come back to judge in the afternoon. In fact, my very first time officially judging instead of just trialing was also the same day that I first tested -- and was asked to retry -- my Preliminary MITF test.
There are other clubs nearby, but it's mostly the same judges, so unless I were going to travel to a distant region, or our club was going to fly in judges from afar, I would not be able to test without knowing any of the judges.
There are only limited human resources in the skating community. Most officials and volunteers are also current skaters, former skaters, or family members of skaters. There are certain obvious conflicts that need to be avoided, but it's not possible to avoid having judges sometimes judge people they know. You just want to avoid judges judging people whose outcome they have a vested interest in. Judges are supposed to recuse themselves from judging a test if they don't feel they can be impartial.