Months between dates
A calendar month runs from a date to the same date in the next month, so 15 January to 15 March is exactly two months regardless of February being short. Leftover days are reported separately rather than converted into a fraction.
How to count months between dates
Financial and legal contexts almost always mean calendar months, not thirty-day periods: a monthly tenancy starting on the 31st still falls due at the end of February. The exception is interest, where many products use a 30/360 day-count convention precisely to make months uniform and the arithmetic simple. If a figure looks a day or two out against this tool, a day-count convention is usually why.
Questions
Count whole calendar months from date to matching date. 15 January to 15 March is two.
It clamps to the end of a shorter month. 31 January plus one month is 28 or 29 February.
Not in a calendar. Some financial conventions treat it as 30 for interest, which is a deliberate simplification.
Divide the days by 30.44, the average month length. It is useful for averages and not for contracts.
Yes; the clamping uses real month lengths, including 29 February.