On jumping, I'm going to quote directly from the 5e PHB, of which I have a dead-tree copy (and note that some liberties, specifically concerning run-up, probably had to be taken due to how the game (and really any point and click game) handles movement). Emphasis theirs, typos mine:
Originally Posted by "5th Edition Player's Handbook, page 182"
Your strength determines how far you can jump
Long Jump. When you make a long jump, you cover a number of feet up to your strength score if you move ten feet on foot immediately before the jump. When you make a standing jump, you can only leap half that distance. Either way, each foot you clear on the jump costs a foot of movement.
This rule assumes that the height of the jump doesn't matter, such as a jump across a stream or chasm. At your DM's option, you must succeed on a DC 10 Strength (Athletics) check to clear a low obstacle (no taller than a quarter of the jump's distance), such as a hedge or low wall. Otherwise you hit it.
When you land in difficult terrain, you must succeed on a DC 10 Dexterity (Acrobatics) check to land on your feet, Otherwise, you land prone.
High Jump. When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier (minimum of 0 feet) if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. In some circumstances, your DM might allow you to make a Strength (Athletics) check to jump higher than you normally can.
You can extend your arms half your height above yourself during the jump. Thus you can reach above you a distance equal to the height of the jump plus 1 1/2 times your height.
Basically, there are no rules concerning weight in jumping, and, horizontally, at least, even a basic character has superhuman jumping skills, if Larian stays true to 5e (though, unless everyone is less than 2 1/2 feet tall, you shouldn't be able to jump over enemies, per RAW and I'm fine with that). This is to keep everyone on the same page. I'm not sure how it translates in-game, without some way to measure jumped distance, but...
As to shoving, yeah, it should take a regular action, instead of a bonus action, again, per RAW.
As a side note, there are no rules about height difference (terrain-wise) in the PHB, so I guess Larian is on its own there. I wouldn't mind the advantage/disadvantage being turned way down and limited to accuracy, but I feel there should be a difference between being several feet above your enemy and several feet below.
Lover of non-haughty elves and non-smutty lesbian romance "1404. I will not spoil the adventure's mandatory ambush by using the cheesy tactic of a "scout"." - From "Things Mr. Welch is no longer allowed to do in a (tabletop) RPG"