Q:

to "sleep" vs to "go to sleep"

I'm from the northeast US.  When describing the phenomenon of going to bed at night, or falling asleep, I always formulate the verb like that, as in "I went to bed at 10" or "I didn't fall asleep until midnight." 
However I frequently hear the formulation "Last night, I slept at 10" or "I usually sleep at midnight".  I'm interested in whether there's any interesting known dialect or historical distinction between the formulations.  I now live on the west coast US and know many people who use these latter forms, and it still sounds wrong to my ear, like it's missing the helper verb (fall, go).  
(The one case where I might crossover is in the sentence "I couldn't sleep until midnight", which sounds right to me, although "I didn't sleep until midnight" sounds wrong.) 

It feels to me (though I don't have the professional vocabulary for this) that for me, "sleep" is an indefinite-duration, continuous action ("I'm sleeping").  So when I want to mark the time that it starts, I need to help it with "go to sleep".  When I hear people say "I slept at 10", it sounds to me like they were asleep for only a moment, at 10 o clock, but not after, if that makes sense. 

A:

I'm a school teacher and have found this quite frequently amongst children of non-native English speakers.  It sounds awkward to me every single time I hear it and I'm pretty sure it comes down to incorrect usage, coming from an incorrect seepage of their family tongue into the English language. 
For instance, I speak some Japanese.  To indicate the time at which one goes to bed, one would use a phrase like "10 ji ni neta" (literally, "10 o'clock at slept").  It makes sense that this structure would be maintained with an incomplete understanding of standard usage of the language.  I imagine that saying "go to sleep" would be misinterpreted as sleep being a destination of travel like "go to library" and therefore rejected as ridiculous.  
The misuse of this verb is not terrible, of course.  Language is here to serve as a means of communication and the loss of "go to" prior to "sleep" makes for little or no loss of that communication.  The worst it does is make for ambiguity of the phrase "I slept late."  Perhaps you can see that it could be taken two completely different ways.  

A:

It's not grammatically incorrect, but it doesn't make much sense.  If someone says, "I did X at 10:00", that normally implies that the activity is something which only takes a short period of time to do completely.  If it's something that takes a long time, we nomrally either say, "I did X from 10:00 until noon" or "I started doing X at 10:00". 
So if someone says, "I slept at 10:00", I would find the sentence puzzling, but if I took it literally I wound understood it to mean that the speaker took a very brief nap, or dozed off for a moment and then was quickly woken up.  I expect someone to say, "I slept from 10:00 until 6:00", or "I fell asleep at 10:00", or "I was asleep at 10:00". 
"Sleep" is not the only word where this applies.  If someone said, "I built a house on Thursday", I would understand this to mean that he was somehow an incredibly fast worker who completed the entire job in one day, not that he began work on Thursday and expects to be at it for many weeks or months. " I read a book at 10:00." " I learned Spanish at 10:00."  Etc. 

A:

I don't live in America, but I don't usually say, "I fell asleep..."
Where I live, there seems to be a distinction. 
"I slept at 10 o'clock" where I live seems to mean that we got into bed at ten o'clock. 
However, we would then specify, "but I didn't fall asleep until eleven o'clock." 
To my ears, there is nothing ungrammatical. 
And, answering your other statement:

"I couldn't sleep until midnight", which sounds right to me, although "I didn't sleep until midnight" sounds wrong.) 

There is a slight difference in meaning to me: I couldn't sleep until midnight  indicates an inability to sleep, whether or not you waanted to. 
"I didn't sleep until midnight" could mean that you were unable to fall asleep as well, but it has an additional meaning of perhaps you just didn't, that is, you maybe sat up late reading a book, and so didn't sleep until midnight.