Learn Finnish: Minä unelmoin pitkästä lomasta.

The verb unelmoida (to dream / daydream) is a cognitive verb that requires the thing you are dreaming about to be in the elative case. Because the noun is in the elative (lomasta), any adjectives attached to it must also match that case, which is why we use pitkästä.

Is unelmoida the verb I use for the dreams I have while sleeping?

No, unelmoida is strictly used for daydreaming, wishing, or fantasizing about something. If you want to talk about a dream you had while asleep, you use the phrase nähdä unta (literally "to see a dream"). Like cognitive verbs, it also takes the elative case: Näen unta pitkästä lomasta.

Why does the ending change from -stä on pitkästä to -sta on lomasta?

This is a quick reminder of vowel harmony! The word pitkä contains front vowels (i, ä), so it takes the front-vowel version of the elative ending (-stä). The word loma contains back vowels (o, a), so it takes the back-vowel version (-sta).

I learned the verb haaveilla for daydreaming. Could I use that instead?

Absolutely. Haaveilla and unelmoida are essentially interchangeable synonyms, and they both govern the elative case. You could perfectly say Minä haaveilen pitkästä lomasta with no change in meaning.