I was employed to work 24 hours per week. After 9 months my hours were cut to 18 per week. 1 month later the office moved 50 miles away and my hours were then cut again to 16 per week. I have been commuting 100 miles round trip twice a week. I have now been informed as of Jan 1st my hourly wage will be cut in half.
Can I quit and claim unemployment benefit?
Yes, I think you should be able to collect as long as you are monetarily eligible and ready to look for full-time work.
Just be sure to document everything when you do quit. Your resignation letter should explain all these changes and you should be ready to back up the changes with paystubs and anything else that proves the quit was attributable to changes in the employment.