Learn Spanish (Latin America): Comí la mermelada muy despacito.

Yes! While you usually see -ito on nouns to indicate small size, Spanish speakers frequently attach it to adverbs. Changing despacio (slowly) to despacito softens the word and adds a cozy emphasis, meaning "nice and slowly."

How exactly does the spelling change from despacio to despacito?

For words ending in an unstressed -io, you usually drop both of those final vowels before adding the suffix. So despacio loses its -io ending to become despac-, and then you add -ito to get despacito.

If despacito already means "nice and slowly," isn't saying muy despacito repetitive?

It is a bit repetitive, but it's very natural in conversational Spanish! Adding muy (very) next to a diminutive adverb just gives it even more emotional emphasis, similar to saying "really, really nice and slowly" in English.

Why use the preterite comí here instead of the imperfect comía if the action was drawn out and slow?