I've been working at my job for the last two years. I've never had a scheduled break or lunch. Often when I try and take a break the boss will have me work. This happens on six hour shifts. I've never had a scheduled lunch/dinner break either for these shifts and also on 8 hour shifts. Am I entitled to take them on my own or can I issue a claim? Can they do this because I'm only partime? I work in a small retail store. These are questions I've had for awhile any information to make my work experience better would be nice.

Heres another qestion. After the week work schedule has been posted, I've gone to work to find out they altered it that same day and expect me to work more than what I thought I was scheduled. Can the employer do that?

Unless you are a minor, then no, breaks are not required.

Your employer is also allowed to change the schedule if they need to.

I read on the Utah Labor Law website that you are entitled to a 15 minute break for every 4 hours of work. Full-day worker needs a 30 minute non-paid break but I haven't been able to find what is considered a full-day of work.

The information that ElleMD gave you is correct for adult employees. The regulations that you came across are most likely the regs for minors (child labor).

Useful links:
http://www.dol.gov/esa/programs/whd/state/rest.htm
http://www.dol.gov/esa/programs/whd/state/meal.htm