Yes it is possible.
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It is 1. Every month contains 28 days.
5 mondays however this only applies on earth, depending on the planets orbit there could be more, for example: Saturn has an orbit of 10 759 earth days in a year, compared to earths 365 1/2 days per year. So taking into account there are 12 months in a "year" there are 896.58333333 days in a month. Therefore there can be over 128 "mondays in a month"
It is a certainty. There will always be at least one month that will meet the requirement.
It depends on how you define sex. If sex is defined as any genital contact for pleasure with another man the answer is somewhere between 1/3 and 1/2 of all adult men. This of course down't mean that these men are gay. In fact, something like 70% of men who self identify as gay have had sex with a woman at least once.
It is 1/6.