Does boosting use more fuel?

Does boosting with a vehicule use more fuel? (Pressing shift makes your car go a little bit faster)

Side question: If it does, what is better for distance? Using the boost and going a little bit faster but consuming more, or not using the boost and going slower but farther?

Yes boosting consumes fuel faster in all vehicles that can boost. I would say if you want to get maximum distance, then do not boost. Reading this Reddit seems to show that you get about double the distance without boosting when observing across a finite fuel range:

BOOSTED, 1 MINI BAR = ~500m

NO BOOST, 1 MINI BAR = ~1km