Well, I meant it quite literally, square as in shape, that means square chin, square cheekbones etc...
If the forehead of a person is the same width as the jaw I believe they would say something like "square jaw" or "square jawline".
дождался something that means that the something you were expecting, anticipating or waiting for, finally happened, or arrived or whatever. That's just it
That's a tough one, I think Russian verbs denoting accomplishment like успеть, дождаться, сходить and many others don't have direct equivalents in English, so the translation would be highly context dependent.
Ex.
Я его ждал, но так и не дождался. = I waited for him, but he never came.
Он дождался что его выгнали с работы. = He ended up being sacked.
Не могу дождаться лета. = I can't wait for summer.
Ты у меня дождешься! = You are cruising for a bruising, mate!