Can someone live in my travel trailer on my property within the county not city limits?
If not, can I use it as my office on a daily basis?
I don't see why not, on either count, but the real answer to check with your local zoning office. In the U.S.A., each village, township, and city have their own zoning codes as to what types of residences they allow to be occupied on a permanent basis, with even more rules if you rent it out. I've never heard of a problem with a trailer office anywhere.
Don't know your exact location so can't tell you any thing
Other people asked questions on similar topics, check out the answers they received:
Other people asked questions on various topics, and are still waiting for answer. Would be great if you can take a sec and answer them