My fiance has been living with me this year and I pay for her food, phone, rent, clothes, etc. Should I claim her as someone I support, and if so do I need receipts?

she is not related to you, so you can't. (otherwise every one in America with a roommate who is not working could be claimed!) 

Once you are married, different story, rules are different. 

To claim an unrelated person as a tax dependent, they must live in your home as a member of your household for the entire year, AND you paid more than half their living expenses, AND they had less than $4300 of taxable income.  This will get you a credit of $500 for an "other dependent."  It will also disqualify the person you claim as a dependent from receiving the coronavirus stimulus payment and certain other possible benefits.