The only reason you would need to know who deleted something is to pester them about it, which would be a pointless annoyance that might even prevent moderators from doing a good job. Admins are the only ones who can restore deleted posts and the only ones who can properly deal with inaccurate mod actions: post in Meta and we'll look into it.
Self-moderation is moderation in addition to global moderation. Both of those posts were insubstantial, so deleting them seems correct.
Bull. If the moderation were serious, instead of removing a bit of humour here and there, and if said moderation was for any LEGITIMATE purpose, then anonymity is contraindicated for the very reasons I stated. It gives the mods the ability to take out a bad day on people for NO reason. I'm not a young man, and I am not gullible. Make a credible argument. Your mods, with a very few exceptions, do not do a good job. They do things like this, and leave scams and libel so obvious that a dead man could see it to go on. One might get the impression they're in on it. Many have. If self moderated threads are not going to be self moderated, then there really is no point to their existence, is there?
At the very least, it would be prudent for the mods to state WHY a post is deleted rather than doing a hit and run. And if anonymity is de rigeur, then at the very least there should be a reply option. Preferably one that goes directly to you, because I doubt very much you would tolerate their general behaviour if you had to deal with the fallout from it. mprep in particular is a weasel. If you are not fully aware of that, just read any five of his posts. His "arguments" don't even make sense in his head, let alone in any sort of open forum.
Short form. If the mods must hide what they are doing, who they are, and why they are doing it, then they are NOT doing a good job and ARE under suspicion of deliberate malfeasance. I generally find you reasonable, but you are totally incorrect on this one except in the fact that you own the forum.