1 干嘛 is oral speak of "做什么“,so ”干“ means ”做“,which is 'do'.
"嘛" most of the time will show you emotion, sometime pleasant, ex. "不错嘛!” ” 很快嘛!“ sometime impatient, ex. "你快点嘛!” (be quick), and the tone of sentence when you speak also show the emotion.
2,3 "点” means some,a little, a bit. So the rule is that if the noun connect with the verb can be "count" with some/a little/a bit, infact the nouns are uncountable or abstract, you can use 点 after the verb.and 点 is abreviation of “一点儿"
你喝点什么?------> 你想喝点什么饮料(yǐnliào drinks), "drink some drinks". the same with "你想来点什么主食" eat some main food. (they are uncountable)
你在图书馆常做点什么?is also right(pay attention to the place, it should before main verb), it is 你在图书馆常做点什么事?do some things. (it is abstract)
so you can't not say 你去点图书馆。(图书馆 can count and is real thing). if you want to say " I go to some library" you use "我去了一些图书馆” (一些yì xiē,some)