Simple and continuous aspect again, which can be either for these sentences as Hungarian doesn't distinguish so clearly between them and/or uses different grammatical structures to get a similar meaning. It seems completely random how these have been translated. The alternative would be "Are you jumping here or there?".
Also, 'ide' and 'oda' would be better expressed as 'over here' and 'over there', as 'itt' and 'ott' mean 'here and 'there.
So if I understand correctly, the you-person is jumping horizontally from A to B and you ask him if he is jumping in your direction or away from it, right? I see a picture of a streetrunner who is jumping from one roof to the other, and on one of those roofs I am standing and asking the runner if he is jumping towards my roof or not. And with Itt or Ott this person would be jumping vertically and landing in the same place, which is either near me or further away. Do I interpret the ide-oda versus itt-ott the right way like this?
"here" and "there" are often used by themselves for destinations of movement as well.
"Come here in the morning". "I will go there tomorrow."
Those sound more natural to me than "Come over here in the morning" or "I will go over there tomorrow", which I would mostly only use if I can see the other place from where I am.
Grammatically no (so now it's accepted), but semantically yes. Since "you are jumping" is present continuous, and it's quite a short period of time when one is in the air, by "jumping" we assume that there are multiple jumps, therefore the hungarian "ugrálsz" shall be used. If it's stated that we are talking about one jump only (or at least without any numerals or quantifiers we assume 1) , or you manage to say this sentence while the actionee is still in the air, then "ugrasz" is the correct one.
This sounds reasonable, but I don't think it accounts for the fact that English speakers use the present continuous in places that your analysis would not permit. For example, two people talking after a concert; one says "how are you getting home?", to which the other responds "I'm getting a taxi".
The particular sentence "Are you jumping to here to there" sounds fine to me, as a native speaker of English. I could niggle about the "to", but it's acceptable. In the right context this sentence means "What is your plan? To jump to here or to jump to there?"