A barmeter would be something to measure a bar with, or perhaps a meter to measure how much alcohol the bar dispenses.
A barometer measures air pressure.
it measures in Bares
there must be vacuum in the mercury barometer because if air enters the tube the barmeter would become faulty as air pressure will change.
Pressure in these things is measured by how tall a column of liquid it can support. Now atmospheric pressure can support many feet of oil, for example, and who wants a barmeter that tall? Mercury is very dense so you can get away with less than a metre high. Problem solved.
there must be vacuum in the Mercury barometer because if air enters the tube the barmeter would become faulty as air pressure will change.