It will be a "pre-existing condition" and will prohibit you from getting STM. You should have applied for the short term medical before this happened. It would be the same as if I had an accident, then the next morning, got car insurance, and demaned they cover the accident I was just in.
I would suggest you shop around for a "mini med", or limited health plan. Some companies that have those are Homeland health, United American, or Mega Life. These are not major medical plans, but are designed for those that don't qualify medically for health insurance. They are also called Association plans. You can google that term, and get a long list.
Probably not based on my experience. The ins co will probably want to see the opinion of a specialist to base the decision on your ability to work.
Now having said that, I have very good ins and they have never questioned my PCP's
referrals to a specialist (and I don't have the issues you have had), nor have they questioned *that* specialist referring me to another. But I did get referred to a
cardiologist (by my PCP for further tests) due to edema and fatigue associated
with my illness.
Hope that helps answer your question.