I want to install a electrical subpanel(~50 amp) in my garage, if I do not feed the subpanel with a breaker from the main service of the house,would or could I tie into the main lugs of the main service to feed the subpanel? (Using the proper wire size) Would I have to use a ground rod for the subpanel?

If your garage is attached to your home you have to have a 4 wire feeder with the equiptment grounds and neutrals separated. But no G rod. If the garage is not attached you can use a 3 wire feed and you will need a g rod. In all cases you have to protect the conductors in your main panel which means you will have to install a breaker. NO DIRECT FEED NO MAIN LUG TIE IN. You have to protect the wire.