All of those phrases are wrong, as it happens.
The correct phrase would normally be "[I am] sorry [that] I am late", but you could also say "[I am] sorry for my lateness". (The words in brackets are optional, but implied if you leave them out — that's just the way the sentences are constructed. And of course you can contract "I am" as "I'm" as usual.)
You can't be sorry (an adjective) for late (an adjective); you can be sorry for lateness (the noun form of that adjective), or for being late, or you can apologize for being late, or for lateness, or whatever. But if you did something a little wrong (being late), you're the one who would apologize for that, not the others. Instead, you could (if you wanted to be rather formal) say "[Please] forgive my lateness", or even "[Please] forgive my delay". But on an MMO that formality probably belongs in in-character/RP chat and nowhere else.
- I'm working
- I am at work
3 and 4 can be equivalent in meaning, just as the first dictionary entry suggests, and neither would be "more" correct. In other words, they can both mean "be busy doing their job right now". The problem is that 4 can easily be understood as 2 in the entries given. So I believe it would come down to context.
If your friend comes into your office, or place of work, and says "Let's play basketball" and you respond, "Not now, I'm at work", then he can see that you are working and deduce from context that you mean "I'm working".
If your friend calls you, or otherwise can't see you, and asks to play basketball, and you respond "Not now, I am at work", then it sounds like you are saying that you are at your office, or place of work. This strongly suggests that you are working, but it's not necessarily true.
In any case, if you want to be clear, I would recommend "Not now, I'm working."
Best Answer
In American English, the idiomatic wording of your sentence when including the time is:
Note that most style guides suggest spelling out numbers less than ten, thus: