Grammar usage

Hey Sanjay, you've asked a lot of questions but I am bored and have no life, so let me try to tackle them all.

I am sorry I am late.

I don't have much to add to my reply to your similar query the other day (http://www.grammarly.com/answers/questions/10853-grammar-usage/#answer_14545) but there is one other possibility I have thought of since I wrote that reply: the sentence I am sorry I am late is correct with no comma because of the optional deletion of 'that'.  I am sorry that I am late means that I regret being late and no comma is needed; that is optional and is often deleted. Otherwise, please see my earlier response.

Irritable/irritated

This is a great question!  Irritable means 'being easily irritated/annoyed', so in your sentence, which describes the reason for the attendees' annoyance, irritated is best.  Irritable describes someone's personality, how they often or usually act, whereas irritated describes how someone behaves in a certain situation.  You may or may not be irritable as a general rule, but in a certain situation you may become irritated.

Hang out

Your sentence sounds completely correct to me. The meaning of hang out in your sentence is 'to spend social time together' and it is an extremely common and quite informal phrasal verb to describe carefree casual social interaction.  To my ear, it is usually only used by people aged 30 and under.  Oh, and was at could be replaced with went to but it is not necessary.

Especially

No, especially is not necessary in this sentence, but it does change the meaning slightly if you include or omit it:

without especially: The sentence implies that the only reason they didn't like her was because they had to wait for her to get ready.

with especially: The sentence implies that having to wait for her to get ready was the main reason they didn't like her at first, but that there were other reasons why they didn't.

I don't really like hang on in this sentence; it may be a difference between British English and North American English, but it seems out of place here.  Hang on has a few different meanings, but there are only three of them that could apply here, and none fit especially well into that sentence:
 

 (a) to ask someone who has phoned you to wait while you call the person they wish to speak to to the phone,

(b) to ask someone you are speaking with to remain calm and not "jump to conclusions", or

(c) to wait briefly (this one doesn't fit well either, because if the waits were only brief, probably no one would have been annoyed, right?).

But I digress...

I hope this helps.