New at growing Tomatoes. If the branches don't have yellow flowers on them they won't grow tomatoes?

The healthy branches that don't have blossoms on them now may well have them a little later if you don't cut them off. If the leaves are wilted on some branches and not others they probably are lower branches. It is normal for the some of the lower limbs to wilt and die as the plant grows and it won't hurt a thing if you trim them off.