Shortly after I got my acoustic guitar, the fretboard was nicked and consequently buzzing sounds arose. This was because one fret was deteriorated/nicked enough so that when the string was pressed on this fret, the next fret up would come in contact with the string when you plucked the string. Hence, there was a buzzing sound. Back then, I took my guitar to a shop and they had the frets sanded down. Recently, I was playing my guitar and noticed that the buzzing sounds actually appear in many places on the fretboard, especially on the higher frets.

How much do fret replacements cost, in general? I'm also slightly afraid of ruining the original wood of my guitar.... Is it possible to replace only the frets without touching the fretboard?

Have you tried adjusting the action just a touch? Maybe loosen your truss rod a quarter turn, see what happens.

Fret jobs can run a couple hundred or more, depending on what the luthier does.

Pull the frets, make sure the fretboard is level and not twisted, plane and sand if necessary, reinstall the frets, level, crown, etc...

A competent luthier will get the job done without messing up your fret board. You have to touch the wood to get the frets out.

Back when you had the fret nicked, you probably should have just had that one fret replaced and leveled and finished to the existing frets.