No. US has lost ONE general in 40 years. With modern communications, there is no reason for a general to be that close to the actual combat.
And two of them were Army Corps level staff officers.
These sorts of people have urgent duties way behind the lines.
Yes.
Again the The US lost 40 generals in WW2.
If the Generals are on the battle field like there Russian Generals seem to be, of course they can die like any other soldiers.
Generals don't have Superman powers. They are not immune to bullets or bombs.