For DB benches, it depends on how you hold the dumbbells. You could do it “bodybuilder” style with elbows flared out and bring them down to the edge of your chest. Or you could do them “powerlifting” style with your hands facing each other and elbows tucked close to the body and bring them down to the chest. I’d go for a full range of motion, but you don’t have to bring them down below your chest.
As for dips, you should be able to make your biceps touch your forearms. If you can’t do that, then you may need to do decline close-grip benches until you are strong enough, or you may have shoulder issues preventing you from doing them through the full-range of motion without pain.