No -- the jump could be beside a monster, passing within 5' of them (assuming 5' reach). There is no need to make this more complicated than the simple examples.
That's weird because it's hard to visualize. Usually, when you are making a melee attack, you're projecting force in the direction of your target. It doesn't make sense to me that you could be moving in a straight line, and maintaining that momentum, while projecting force perpendicular to your movement. In that scenario, it's more likely that you're
actually coming to a stop - or at least slowing down - before you make your attack.
Again, No, because you also have an action on your turn. Only if you move 60' in a round you are literally moving for the full 6 seconds (though you still have a reaction and a bonus action, so it's not literally "literally").
If you're taking the Dash action, then you're actually
dashing. By focusing your effort on
just moving, you're able to travel
faster than if you try to do other stuff while you're running. Your movement speed is how far you can move during six seconds, while doing other stuff. It's not like Actions take 3 seconds and Movement takes 2 seconds and Reactions and Bonus actions each take half a second; your Movement takes six seconds, and all of the other Actions you perform also take six seconds.
D&D combat occurs in turns, that are tightly regulated by the initiative sequence. We both know that. My post above to Caliban answers this.
For the purpose of mechanical resolution, combat sequence is governed by the turn structure. Within the
actual game world, movement is continuous.
The rules for jumping are written from a common-sense perspective, using natural language. If you want to make a long jump, then you need a running start. It doesn't matter whether that movement occurred on your previous turn, or your current turn, as long as you have your running start before you make the jump.
If it helps, imagine that you have two runners crossing a 60-foot field, followed by a 10-foot crevice at the far end. One of the runners is a dwarf (speed 25), the other is a human (speed 30), and both have Strength 10. By your logic, the dwarf would be able to jump across the crevice on their second turn by dashing 50 feet in the first round and then moving ten feet before jumping; but the human wouldn't be able to make the jump without slowing down or doubling back, since dashing 60 feet on the first round puts them right at the edge of the crevice with no room to build speed. And that outcome doesn't describe a situation that makes sense - the human
should be able to make that jump while continuing to run in a straight line.
Unless you want to argue rules as physics, that combat rounds
aren't an abstraction, and that characters are
aware that it's possible to make a long jump after running for 4 or 8 seconds but not after running for 6 seconds.
