You might not need jQuery
No, please no.  If size is an issue for some reason or you want to have no dependencies you can use something like http://zeptojs.com/ and just embed everything in one minified file. If you do things right only the functions you are actually using will get placed in there as well.Do not reinvent the wheel to solve problems that can't be solved in much cleaner and nicer ways.  Managing dependencies can be annoying, but we all bite the bullet for a very good reason, because reusing solid well tested code is a good thing.