#1
Grace notes are like little small notes added onto another note and are played really fast, but don't have a specific time amount.
Say there are 4 quarter notes and the last one has a grace note attached to it. You'd have to stop the 3rd quarter note that tiny bit early to fit in the grace note so you don't mess up the whole timing of the song by having this one bar that is 4 beats + this extra tiny bit, right?

Also, when listening to a song, would there be any way of knowing which notes are grace notes and which are normal, but just really fast notes?
#2
It depends. If the grace note is BEFORE the beat, then yes you would stop the 3rd note short. If it is ON the beat, you would stop the 4th note short.
#3
The grace note would start on the beat that it is attached to, I believe. In response to your second question, on paper grace notes are just for convenience.
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#4
A grace note (acciaccatura is the proper term although appogiaturas look and sound similar) is nearly always played a bit ahead of the beat so that the note lands directly on the beat.
#5
Quote by Ockeroid
Also, when listening to a song, would there be any way of knowing which notes are grace notes and which are normal, but just really fast notes?
A grace note would be something like -5h7- when you hit the 5 and quickly (and I mean fuckin' fast!) hammer to 7. If you see reason to write something with a specific note value, put in that note value. If it's just fast but no specific amount of time needs to be noted, then it's a grace note.
#6
Technically the grace note is unaccented, and the note following it is accented. Therefore the accented note should be on the beat, and the grace note should be very slightly before, which does make the previous note a negligible amount shorter.