What’s the difference between cracked and coarse rounded black peppercorns

Yes, the white pepper is the whole black peppercorn with the skin removed (and possibly fermented via a water soak). A lot of the pepper flavor is in the pepper skin (the black part) which is removed in the process of making white pepper. The compound that gives pepper its flavor is piperine which isn't found in the pepper berry as much as it is in the skin.

Well, I've never had whole black peppercorns dissolve. In very long cooking, and depending on the variety and age of the peppercorn, they can soften somewhat. But when adding whole peppercorns to a dish, I either plan to remove them after cooking or be prepared to bite into a serious bit of pepper every now and then. To avoid this problem, I generally at least "crack" or crush the peppercorns a bit if I intend them to be in the final dish. (This aids in softening and seems to allow the flavor to blend a bit more, though large bits can still be very peppery.)

Black pepper tends to lose a lot of subtleties of flavor quickly once it is ground, which is why pepper grinders are so common in restaurants (and at home). There's no advantage of using pre-ground pepper in a soup or stew, but I definitely tend to grind it myself right before adding to avoid the large chunks of peppercorns. (Different varieties of peppercorns can vary a lot terms of potency, especially when they are fresh, so perhaps yours are more mild than the ones I generally use and thus less noticeable when in larger chunks.)

Some people buy pre-ground pepper and find it convenient, though. My one caution, if using pre-ground pepper and you desire a very peppery dish, is to not overdo it. Whereas whole peppercorns will gradually release subtleties of flavor, pre-ground pepper can change somewhat quickly from barely noticeable to a burst of strong pungency.