With go, or verbs that can be interchanged with go, such as drive, walk, move, etc., sometimes the relation between the destination and speaker can be expressed with either verb.
I went down to the store.
I went up to the store.
Do we consider the store "down" or "up" from us? Assuming the store is not significantly downhill/uphill from you, it doesn't matter too much. In my opinion, "down" may have a bit of meaning of "forward" or "in front of," - something I've commonly heard is "I'm going to walk down this path" when you really mean "I'm walking forward along the path."
Conversely "up" will have a bit of meaning of "behind." This isn't really a hard and fast rule and could vary widely depending on region.
The implication in using either word is that a bit of a journey was involved or will be involved.
Native speakers would understand either way, unless the "X" in "I went down/up to X" is physically higher or lower than you. Saying "I'm going down to the third floor" when you are on the second floor will confuse people. Saying "I'm going down to the restuarant" will not.
In A4, assuming a situation of theater seats where they are all in a row (none are really "up" or "down") - you could substitute "up" and not really change the meaning, though "down" sounds more natural.
A4. Would you mind moving (further) up so that we can sit here, too?
Regarding 5a, "up" or "up to" can also mean "near," particularly with words that involve the subject moving items (pull up, push up), or the subject moving himself/herself/itself ("up to" will be used - ran up to, walked up to, etc.)
Strictly speaking, the sentence is incorrect because listening of playlists is ungrammatical (unless the playlists are doing the listening). Since categorization takes of and editing takes of but listening takes to, you have to write this:
Some websites allow categorization of, editing of, and listening to playlists online.
This is grammatically correct but it sounds very clumsy. If each noun took the same preposition, you could use the same preposition for all three:
Some websites allow categorization, editing, and playing of playlists online.
This is grammatically correct but it sounds even clumsier because of the repetition of play. People would rather make a subtle grammatical error than write a sentence that sounds this clumsy.
The fact that the first two of the nouns take of probably led people to ignore the incorrect listen of for almost ten years now.
Another “fudge” solution is to choose the preposition to agree with only the nearest noun even if it disagrees with all the others, known as “proximate agreement”:
Some websites allow categorization, editing, and listening to playlists online.
There is, however, a better way:
Some websites allow users to categorize, edit, and listen to playlists online.
This is clearer because the users are mentioned explicitly, and the nominalized verbs are replaced with plain old infinitive verbs. The preposition to only agrees with listen, but that's OK: categorize and edit are transitive verbs, which take an object without any preposition at all. So, to connects only with listen and there is no disagreement with categorize and edit. So, this version has perfect grammar as well as greater clarity.
By the way, many gerunds do take of. For example: editing of playlists, feeding of animals, planting of gardens, singing of songs, etc. Also, gerunds normally function as nouns. In the original sentence, editing and listening are objects of allow, just like categorization.
Best Answer
Fall victim to is a complete idiom in English and is generally used with diseases, disasters, and other catastrophic situations. Otherwise, use victim of.