I've heard various ideas such as limiting it only after mods have expended their points (this will require implementing a cooldown to prevent a user from getting points again too soon). I want to hear your feedback, and I'll roll together something for the next major update of the site. Leave your comments
I don't think a) is a good idea. Quite the opposite: I think it would be sometimes worthwhile to be able to both moderate and say in a reply why you moderated that way.
The only problem that can arise from this is "comment highjacking" to get a prominent position without the parent post shown, but I think that should be addressed differently.
One possibility would be to have replies to hidden posts be shown in the position where they would be if the hidden post weren't there, that is, if you moderate a post down to invisibility and answer to that post yourself, you'll get a position where your post would have ended up if you had replied to the parent of the post (or if posted top-level, if the post you replied to was a top-level post). This would remove the incentive of "comment hijacking" (and also would solve the problem for those cases where people reply to an already modded down post in order to get a high position, which cannot be solved by moderation restrictions art all).
BTW, in relation to this: A feature I always had wished for is an option to always show the parents of displayed post, possibly collapsed but definitely not hidden, even if otherwise the post would have been hidden. The lack of that feature is the main reason I currently browse at -1 and just actively ignore any unwanted stuff.
For (b) I have no idea what problem is to be solved, but I wouldn't object to that; I can imagine it hard to implement though.
For (c), I fully agree.
And of course, for completeness there has also to be
d) You certainly should not be allowed to moderate your own posts.
This is currently automatically covered by the rule of no moderation in stories you posted to, and therefore might be a trivial case to overlook; therefore it deserves an explicit mention although I'd expect it to be completely uncontroversal.
BTW, Congratulations for the Soylent team to the design update. The site definitely looks better now! (I cannot say much about the functionality yet, but I'm sure it's much improved, too.)