1. No, don't focus on doing 3 and 4 board presses. As a beginner, your sticking point is probably still very low in the bench. I recommend that you perform a wide range of max exercises just to get a feel for them if nothing else.
2. Eventually you'll get a feel for all the max exercises and know which ones you're best at and which ones you need work on. These are things you just sort of learn along the way with westside.
3. Are your tris weak? Probably. Just saying that your tris are weak doesn't mean much though -- since they're so involved in the BP, most of the time your tris are going to be the weak point.
4. More likely your problems starting out are going to be lats and speed. You bring up lats by training them 3x a week in the same plane as the bench -- and you bring up your speed just by following the westside routine with your speed days.
My advice to you as a westside beginner is to just relax -- try everything out a few times before you start flippin out. And do less work better. And as always, keep asking questions and learning.