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.
Regarding the use of in with time:
There's a couple of common expressions that use in with time (there's probably more than below):
In time - means before an understood deadline of some sort. It differs from on time - on time means you arrived at the correct time - in time may mean you got there early.
("In time" can mean "when circumstances allow" or "eventually" - it will usually but not always start the sentence, or precede the subject-verb part of the sentence, i.e. In time, we will conquer the enemy or *If you keep working at it, in time you will succeed.)
In plenty of time - means with an ample amount of time left over.
For in time and in plenty of time, the point of time that you arrive is "within" or "inside of" the range of time you have to be at the destination, so "in" makes sense.
Let's say we are talking about a train - the train leaves at 5:00PM, and you learned of the train leaving then at 3:00PM. You arrived at 4:45PM. 4:45PM is in the range of 3:00PM to 5:00PM.
Some others:
In good time - equivalent to in plenty of time (people racing one another comes to mind with this)
In enough time - when something is ready - The cookies are baking. In enough time we can eat them.
In no time - means something has taken no time to happen, or a very short duration of time passed. - I was driving recklessly and got to the station in no time.
So...
I like getting to the station in plenty of time.
I like to get to the station in plenty of time.
These sound fine to me, but are something you'd hear in speech more than see in writing in my opinion.
Regarding the difference between getting and to get:
In my initial opinion as a native speaker, there is not a difference between them. However, this says the following:
Using a gerund (-ing form) suggests that you are referring to real activities or
experiences. Using an infinitive (to X) suggests that you are talking about
potential or possible activities or experiences.
So, since you are talking about a potential activity, to get is the right thing to use.
Best Answer
"Cumplir promesas"
There is no single translation that will work in all cases. I won't cover all cases here: I will concentrate on how to specify definitions but mention a few related points.