I have a bucket with 500 marbles of 6 colors (reb, blue, green,
yellow, black, and white) and three sizes (big, medium, small). I want
to know whether there are an equal # of marbles for each color (i.e.,
16% red, 16%, blue, etc.).

1) What test should I use and what should my sample size be?

2) If I suspect red marbles represent 32%, blue 8%, green 8%, and the
other colors 16% each, what test should I use to confirm this
suspicion and how large a sample do I need?

3) What test should I use if I want to determine whether color
statistically varies by size (e.g., red marbles are more likely to be
of small size)? What sample size do I need?

500 marbles! -- I would just dump out the bucket and count/sort them
all...why bother with samples?

The marble example provided is an analogy for the actual problem.  For
exposition purposes, let us assume it costs $100 to count each marble.