Do insurance requirements vary from state to state? (For example, are the insurance requirements the same in Texas as they are in California?)

Unfortunately, there is no state-to-state consistency.  The Uniform Condominium Act (UCA) was drafted in 1980 by the National Conference of Commissioners on Uniform State Laws to provide the needed uniformity, but the current law pertaining to condominiums remains incomplete in most jurisdictions.  Even those jurisdictions which have pioneered condominium legislation have not developed fully comprehensive acts.