Automatic driving – general

Hello, I drive an E90 320i (150hp) automatic and am quite unsafe/afraid about the operation. On the one hand I drive my car gently warm or I try it. However, I am almost paranoid when it comes to giving gas. If I push the pedal too fast or deep down, it immediately switches down 1-2 gears and turns up, then I panic that with the still cold engine what happens. On the other hand I do not want to s Another problem, on the way home the highway starts from 1km away and since I don’t want to turn up like anything else, because the engine is practically cold, I sneak along the acceleration lane and immediately turn up at the speed 90 to the trucks on the right track. The car feels quite sticky in normal D mode (until you give gas), but in the D/S immediately much lighter, but the extra consumption then scares me off. Do you see that? How do I go with the automatic?