They overlap, but they are not used in exactly the same way.
Désolé ! = Sorry!
Often expresses regret or apology.
Pardon ! = Sorry? / Pardon! / Excuse me!
Can be used when bumping into someone, or when you did not hear something.
Excusez-moi ! = Excuse me!
Often used to get attention, pass by someone, or apologize politely.
So:
Yes. If you are the person who is sorry, the form still depends mainly on your gender, not on how many people you are speaking to.
So:
If a group is speaking, then the form can become plural:
But for the single-word exclamation, learners most often need just:
You capitalize it only if it starts the sentence, as in Désolé !
In the middle of a sentence, it would normally be lowercase:
So the capital letter here is not special; it is just because the word stands alone as the whole sentence.