If you want separate terms to refer to 30-day months and 31-day months, I doubt you'll do better than 30-day months and 31-day months.
Even and odd sound nice, but they have an unfortunate flaw: people use them to refer to even- and odd-numbered months! That is, months 1, 3, 5, 7, 9 and 11 are odd; months 2, 4, 6, 8, 10, and 12 are even.
The term knuckle month sounds nice, too, but not everyone will get the reference, I'm afraid. I'm certain of this because I just talked to a friend a couple weeks ago who was unfamiliar with the knuckle mnemonic.
You can, of course, use a term like knuckle month or odd month, as long as you're careful to tell people what you mean by it. But if your goal is to communicate without further explanation, I would avoid looking for special terms like these (fun as it may be) and simply state the number of days.
A good word for the first type of person might be blowhard: An exceptionally talkative and boastful person. Or, perhaps they are a windbag: someone with nothing to say, who takes all day to say it.
Going only slightly further afield, you might call them a blatherer, babbler, prattler, or chatterer.
Best Answer
There's the word gyro, which, according to NOAD, is:
Your picture doesn't look like a gyro, though, because of the bread. Usually, I'd expect a gyro to look more like this:
However, that's the closest commonly-used word that I can think of.