First, some context. Desdemona has just asked Iago how he would praise her. So he replies:
I am about it; but indeed, my invention
Comes from my pate [etc.]
What Iago is saying is that though he is trying to come up with a creative response, his creativity ("invention") is not sharp enough. He says creativity comes out of his head as easily as birdlime comes out of woolen cloth—i.e., not easily at all. Just as trying to remove birdlime stuck to frize would cause the wool itself to be torn out along with the birdlime, Iago claims that he finds being inventive so difficult, the effort pulls his brains out from his head.
To answer the second question, an explanation of "wit" is in order. "Wit" in Shakespeare's day meant something more than the aptness for quickly making clever jokes that the term implies today. It implied the ability to see deep connections between superficially unalike things. The Old English verb "witan" meant "to know". As a noun, "witan" was a plural meaning "wise men" or "sages", specifically those who were members of the witenagemot, an advisory council to the king. (Now you know where JK Rowling got the word "wizengamot".)
So when Iago uses "wit", he means it as the noun form of "wise", just as "fairness" is the noun form of "fair". In fact, the words "wise" and "wit" both come from Old English "witan". Iago says that of the two qualities a beautiful and intelligent woman such as Desdemona has, one of them ("fairness") is to be used, while the other ("wit") uses it. That is to say, an intelligent woman will know how to put her beauty to good use to achieve her ends.
Of course Iago is being falsely modest when he says he's not intelligent or creative enough. He is the most cunning character in the play, and his dissimulation here reveals his deceptive nature. His response to Desdemona boils down to "oh, you're smart enough to know how to use your looks to get what you want"; it is basically an insult disguised as praise. So this passage reveals his misogyny as well.