Is everybody eligible for "Short Gap" health care exemption, meaning if you don't have health care for < than 3 months you do not have to pay any Tax penalty?

Yes.

You are allowed one gap per year of up to 2 months (one day of insurance in a month counts as an 'insured' month).

The sort-of exception to that is if the 'gap' spans two years and is more than 2 months.  For example, if you did not have insurance in November, December, and January, the first year would qualify for the 2 month 'gap' exemption, but the second year would show a penalty because it is the third month.