The problem with future "tense" is that we need to construct it out of other grammar - we don't have a set "future tense" form, ie. future verbs. "To be about to" means the action is moments away. As the other members have explained, the different ways of constructing the future have very different meanings and uses, so it's best to take the time to learn them properly.

"About to" means in the instant or very near future, "Will" tends to be used for indefinite future plans. Present continuous for fixed plans. Also I would usually say "to go to sleep" (and in these examples "go to bed" is better) If someone calls you on the phone you might say "I'm sorry, I'm about to go to sleep" I will go to sleep when the TV programme ends. I'm going to go to sleep at 11pm.

Actually, none of these are the same. I'm about to do something = I've already decided to do it and I'm going to do it very shortly. "will" is not the same as "going to" You really need to work with this stuff a while to get used to it.

A note about will and shall. Normally in MY variety of English it should be 'I shall sleep' but 'will' emphasises, and 'I will sleep' becomes like 'I definitely shall sleep'. Shall and Will are modal verbs. Shall is first person and Will 2nd/3rd - normally; but when stressing, the usage reverses and so 'He shall not sleep' vs 'He will not sleep' the first emphasises certainty. But this 'rule' of grammar is much relaxed and 'will' is commonly used in any person, 'shall' conveys intent now.