As long as you use the delay(...) function you are likely to have the problem "...I am unable to make it so that you can press the other function buttons while another function is being carried out...".
Use millis() instead, but you will have to structure your program differently.
The examples listed by gfvalvo are a great place to start.
delay(...) should come with a big warning along the lines of "The delay(...) function is likely to get you into a lot of trouble. Unless you are an expert, use it only for demonstrations, toy programs, and debugging."