>1. Any function to check a defined menu?

Check out the Set Mark Of Command in the help file...

>2. How to specify the font, size and style for a menu in menu designer?

Both the Define Popup and Define bar have a font clause. The following shortcut menu code was produced by the menu builder. I hacked the MPR and added the font clauses myself since you cannot do this in the menu builder. I think GenMenuX - from Andrew Ross MacNeill supports directives to handle this through the builder:

DEFINE POPUP shortcut SHORTCUT RELATIVE FROM MROW(),MCOL()
DEFINE BAR 1 OF shortcut Font "times new roman",14 Style "B" PROMPT "one"
DEFINE BAR 2 OF shortcut Font "arial", 24 Style "I" PROMPT "two"
DEFINE BAR 3 OF shortcut PROMPT "three"

ACTIVATE POPUP shortcut