Avenge is to get revenge for someone or something else, usually. If I want revenge for my father's death, I will seek to avenge him. Avenge is generally a verb, and revenge is a noun, or occasionally an adjective. I'm not sure what that expression is, but avenge angel I would take as an angel avenging someone, whereas revenge would be one getting revenge? Neither one makes a whole lot of sense to me, though.

Maybe instead of completely we could use "truly." Quite doesn't mean extremely, but it is definite. Sometimes we use pretty in a similar way. He's pretty good, or it's a solid score. He is actually good, and not just a tiny amount. Very, though, is extreme. Yes, if using them as qualifiers, quite would be less than very, but more than a little.

I think if you ask someone how to pronounce it, they will do a full unvoiced pronunciation of ths. Merriam Webster backs me up: http://www.merriam-webster.com/audio.php?file=month002&word=months&text=%5C%3Cspan%20class%3D%22unicode%22%3Eˈ%3C%2Fspan%3Emən(t)s%2C%20%3Cspan%20class%3D%22unicode%22%3Eˈ%3C%2Fspan%3Emən(t)ths%5C However, as to how we say it normally, I think you're right that it's not so clear. I don't know how to explain it linguistically, but I think we say mon and then the s with our tongue in the unvoiced th position. It's kind of a lesser th, but I think there's still a trace of it there. Does that help?

A profile is a view from the side. So if she turned sideways, she looked the same as looking at a sharp axe. She was so skinny she almost disappeared when she turned sideways.

You can say your bootlaces are untied, but at least in American English I think the most common would be to say your shoe is untied. You could, though, say something like, "Oops, my laces are untied. Hold on while I tie my shoe." Boot would work, but the phrase we tend to use is using shoe.

It was never moved from its correct position even a tiny bit. Off of its place by even, you could say.

I've heard people say the "rat-a-tat-tat" of a machine gun.

I would take this as would you please make some stew for me to eat, but depending on the context, there is another possibility. To stew is to worry or be angry about something for a long time. I think it's possible, but seems a little awkward, to mean, "are you going to make me fret about this?" Again, that would require the context to make it mean that.