What would happen if we didn't have the Supremacy Clause?
I can only speculate as to your first question. In general, there would be more litigation to resolve disputes.
The answer to your second questions depends on state law. The rules of some federal and state courts or administrative agencies may permit a paralegal's appearances at hearings on behalf of a party. In other jurisdictions, the paralegal could get into trouble approaching the bench.
The following is an example from a CA statute:
(a) It is unlawful for a person to identify himself or herself as a paralegal on any advertisement, letterhead, business card or sign, or elsewhere unless he or she has met the qualifications of subdivision (c) of Section 6450 and performs all services under the direction and supervision of an attorney who is an active member of the State Bar of California or an attorney practicing law in the federal courts of this state who is responsible for all of the services performed by the paralegal. The business card of a paralegal shall include the name of the law firm where he or she is employed or a statement that he or she is employed by or contracting with a licensed attorney.