Q#1: IDIQ are non binding contracts with specific clauses that are established to provide quantities or services and/ or supplies and mostly are broadly written. The Small Business in question should have that “contract” with a government entity before a Task Order can be issued. Agencies do either multiple or single award IDIQs all the time.
Q#2: All companies that are awarded or supposed to do work under that Multiple Award IDIQ shall be given opportunity to compete. Elegibility is established upon the award of the IDIQ contract.
Q#3: Size status is determined prior to award, and for Small Businesses, only the SBA can certify their elegibility and size.
FAR SubPart 16.5 will give you most of what you need to know. A little reading will go a long way, specially if you are new to the trade.
Hope this helps…