1. It's a standard 1st conditional.

It is the first conditional case! There is construction for instance "If I do something better I will achieve good results"

They are both correct, but have different meanings. #1 means if an event ("that") occurs, "that" action will make "him" happy, and as a result "I" will be happy also. #2 means that if "I" am happy, my gladness itself (my gladness would be the event) might cause "him" to become happy. The sentence is saying that the writer will make himself glad (in outward appearance, at least) in order to make the other person happy. #2 is a hypothetical future conditional situation, or possibly would equal the subjunctive case in your language.

The first conditional form is: if + present simple, ... will + infinitive. The "if" clause can come at the beginning of the sentence or at the end. Therefore the correct answer is, "If that makes him happy, I'll be glad," OR "I'll be glad if that makes him happy."

I think 1,because when we use the word "if" we should not use also "will"