1. How many programs are you allowed to rank/apply to?
As many as you want, granted you want to pay for it all. Applying to programs is separate from "the match", which you fill out months after you apply to programs. You'll most likely apply to more programs than you wind up ranking for the match.
2. Can you apply to whichever program you want?
Yes, you can apply to any program and any number of programs. You can, in theory, apply to 5 anesthesia, 5 emergency medicine, and 5 family practice programs, then rank your choices of rank as
#1) Anesthesia at Hospital A
#2) Emergency Medicine at Hospital B
#3) Emergency Medicine at Hospital C
#4) FP at Hospital D.....
etc etc..... you can rank in any order or specification you want, but applying to such varied programs is not advisable usually.
3. If you apply to Allopathic residencies how does that affect Board Certification and Liscensing as a DO? It doesnt. Most licensing boards dont know whether your an MD or a DO. A license is much different than a degree. In most states your liscense will say "License to practice medicine and surgery"... and nowhere will it mention the words MD or DO. Now, in 5 states (PA, FL, WV, OK, MI)... you're required to do an osteopathic rotating internship for licensure. This is less an idea of the licensing board as it is a product of these State Osteopathic Medical Societies who in essence lobby for these rules in order to retain their "osteopathic identity". That said, the AOA is becoming more forgiving and granting waivers to those who apply with good reasons to have their first year of allopathic residency count as their osteopathic internship.