Shouldn't it be written a comma after "όχι"? I thought it was a negation ("no excuses").
Yes, of course. These sentences, however, cannot be edited at this point so they stand there laughing us. It was a slip up. Sorry,
You are correct, the negation would be Δεν λυπάμαι. Όχι only means ' No' , not 'not'. In the subjunctive 'not' is μην.
Μην + subjunctive is also used to form the negative imperative: Μην καπνίζετε! Μη φοβάσαι! Μην τρέξεις!
"Οχι" means "no" so it wouldn't fit. For "not" we would use "δεν λυπάμαι" I am not sorry". It's very positive that you are using the words and asking. That's the best way to learn.
I don't think so. To ask someone to "excuse you" is not the same as being "sorry". "Excuse me" means someone should 'overlook' your behavior while "sorry" shows your 'feelings' about your behavior.
"συγγνώμη" is "sorry" as well as "excuse me" whereas "λυπάμαι" is "sorry for something that I caused, or something that happened to you.