DON'T IT HURT= In standard English this should be "doesn't", but in colloquial English some people use "don't" for all persons. The sentence "doesn't is hurt?" is a rhetorical question (= a statement that is formulated as a question but that is not supposed to be answered), so it simply means "it hurts".

DON'T IT PAIN...= Doesn't it hurt...
Another rhetorical question. The use of "pain" as a verb is not common, but possible. We usually prefer other verbs such as "hurt" and use "pain" as a noun (if I hurt you I cause you pain).

SILENCE IS GOLDEN= Silence is very important; it's something precious (it's important to be quiet and not say anything).

BUT MY EYES STILL SEE= I must be quiet and not tell her what I know (that her boyfriend is cheating on her), but I'm not stupid, my eyes still see what's happening (I know the truth).
By the way, if you cheat on your lover, you secretly have some kind of sexual approach with another person.

TALKING IS CHEAP= (Proverb: talk is cheap) It is easier to say you will do something than to actually do it. (Saying this in response to someone who promises you something implies that you do not believe that person will keep the promise.)
- Jared told me he was going to come and help me, but talk is cheap.
- You always say you're going to take me to Venice. Talk is cheap.
In the sentence "talk is cheap", the word "talk" is a noun, it means the act of talking, speech. In the sentence "talking is cheap" we don't use the noun, but the verb "to talk", and when a verb is used as subject of a sentence it goes in the –ing form:
- Dancing is wonderful.
- Cheating is a terrible trechery.

PEOPLE FOLLOW LIKE SHEEP= People are uncritical and easily believe what others say. If you like a politician, you support him (we can also say that you "follow" him). If the politician deceives you and tells you lies and you believe him and support him, you follow him like sheep (uncritically, without reasoning). In this song the one deceiving is not a politician, but her lover.

HOW COULD SHE TELL?= (this is another rhetorical question) It is impossible for her to know what's happening = she can't tell.

PITY!= It's a pity, it's a shame. You say this when you think a situation is unfair and/or makes you fell sad about it.

FALL FOR HIS LINE= If you fall for something, you believe it without reservation. In colloquial English LINE is insincere talk, usually intended to deceive or impress. So to fall for his line means to believe his lies.

KEEP COOL= Act with your head rather than with your heart.

MIND YOUR BUSINESS= Don't interfere with other people's life, leave people alone.

YOU FOOL= When you insult someone, using YOU gives more emphasis (so "you stupid" sounds stronger than simply "stupid"). The words "fool" or "silly" are insults, but they sound too childish so it's not really an insult when used by adults. Here, the singer is reprehending himself for thinking about acting foolishly.