|"Does razer gameboooster work?"|
What is does is shutdown any background apps that may be slowing down the system, so in that sense, yes, it works. Will it help in your case? Probably not. But it won't hurt to try.
"any other alternatives for improving FPS would be fine"
Nothing will help other than to buy a laptop (or desktop) with decent gaming graphics. No software program can make up for the weakness of the Intel HD 3000. But looking at the system requirements, Minecraft should be playable. Try lowering the game resolution.