I was wondering if when I level up and choose certain abilities will I still be able to choose from others I did not pick? Are the options you get to choose from lvl dependent, like after I level to level 2 will the options for level 3 be different?

 

I am wondering if the things I do not choose disappear or can I potentially choose them later?

You can chose them later (at other levels).  Some of the times better options open up as you go p levels, which would make choosing the earlier stuff non-optimal.