Do nihilists think they have no goals (aka terminal values) or do nihilists think they don't have goals about fulfilling others' goals or is it something else?

I am not a nihilist, and I don't know if I'd be able to pass an Ideological Turing Test as one, but to give my best answer to this, the nihilist would say that there are no moral oughts. How they connect this to terminal goals varies depending on the nihilist.

Ok so would that be right to say this?: Utilitarianism is giving equal weight to everyone's utility function (including yours) in your "meta" utility function. Egoism means you don't consider others' utility function in your utility function.

The first part, kind of, the second part, no. The utilitarian holds that the right thing to do is determined by what maximizes world utility, which is produced by utility functions. All utility, including your own, is given equal weight in the "moral decision" function. As for egoism, it simply means that you consider others' utility functions to the degree that they're a part of your utility function. It doesn't mean that you disregard them altogether.