This is with an awful lot of assumptions which are not really viable by any science.
Assumption 1: You can "simply" scale it up (because Ultima Thule is guaranteed to be smaller)
Assumption 2: When scaled up Everything thats effecting the shape ignores the shape but
works outside of it as if nothing changed (not feasible to any extend in the real world)
- North: The top end of the Object (when viewed from the Picture)
- South: The bottom end of the Object (when viewed from the Picture)
- Merge: The point where the two Parts meet
Would change dramatically depending on how far away you are from the Merge as long as you are the same distance away from the merging point Gravity is consistent. (Assuming even density through out the Object)
There are two "peaks" in gravitational force one when on the south and one on the North although the north peak force is weaker than the south peak force. (because when in the south you are closer to more mass than when in the north. (Assuming same density for both Parts)
The lowest gravity is a little north of the Merge as the smaller part is closer and thereby pulls stronger per kg on the observer than the bigger part and can because of that cancel more force from the larger object out. It also could be that there is a point between the two parts where the gravitational pull is not towards the ground but to the left or the right of the observer. (Assuming left or right are defined by where the ground is and not where the gravitational pull pulls you toward)
Water would pile up a bit to the south of the Merge. Anywhere else you would find only very small pockets of water (pond size) if at all.
Atmosphere would behave similar to water with the difference being that you would probably find everywhere at least a little bit of atmosphere gases. Because of the uneven amount of atmosphere around the object pressure near the Merge would be way higher than anywhere else. (This would be counteracted to a degree by the lower gravitational pull near the Merge)
The rings we see on our own earth because of difference in surface temperature would be way thinner and not only caused by the temperature difference but by the differences in atmospheric pressure and gravity.
When given rotation (and rotation speed) and distance from the star as well as star type
(and age) I could give basic predictions about weather and flora/fauna.