I am an F-1 student and have been in the U.S for the past 4 years (almost). Can I qualify for any kind of residency (such as State residency?) or can I be claimed as a dependent? Thanks!"

Every state has its own requirements for "state residency". Please clarify as to what you mean by "can I be claimed as a dependant?" tax purposes?

If I'm living with a family member who is a permanent resident (not parents), and he/she covers most of my expenses. Can they claim me as a dependent?

Where can I find more info about State residency? I reside in the State of Florida.

Thanks for all your help!

No, to be able to claim you as dependent for tax benefit, you must be US resident.