Learn English – “found in the list” or “found on the list”

First, "of my heart" simply means that something is associated with your emotions:

You are the love of my heart.

Also, when we use words like "heart" or "head" metaphorically, prepositions may not mean what you think they mean. Consider:

You really got in my head for a minute there.

That simply means, "You affected my thoughts," and (thankfully) has nothing to do with you shrinking and climbing into my skull.

As for "of my heart" vs. "in my heart", here's one way I might characterize the two:

• of my heart can be used with the definite article, to indicate preeminent personal feelings
• in my heart can be used with the indefinite article, to project a role

For example:

You are a diva in my heart. (means: in my heart, I regard you as a diva)
You are the diva of my heart. (means: in my heart, I regard you as the diva)

So, back to what you said:

"of my heart" sounds like you have several hearts, and one of them is your champion...

Instead:

the champion of my heart

means something more like:

there may be several people who could be my champion, but, in my heart, you are my true champion

Disclaimer: I wouldn't regard this as a hard-and-fast rule with zero exceptions. As was mentioned, prepositions are very tricky. Macmillan lists more than 20 possible usages of the word of, and when you combine those with metaphorical words such as head, heart or skin, some preposition-noun combinations will indeed be idiomatic, and need to be learned one-by-one (such as, "She really gets under my skin.")

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.