at night, during the night

[joham]

Dear sir,
I'd like to ask a question: Is the phrase at night used only for a regular event? like in:
Bats come out only at night.

We say: I couldn't sleep last night/ during the night. But I wonder if we can also say: I couldn't sleep at night(meaning last night)? or:

I was still awake at 2 o'clock at night (meaning last night).

And can the phrase during the night be used for a regular event?

[Niall]

During the night can be taken to mean last night or at night, so it can be used as last night or to describe a habitual action or a regular event.

At night cannot be taken to mean last night, and can only be used to describe a regular action.

[joham]

Dear sir,
Then can I say: I woke up at 11.40 at night. ?
I woke up twice in the night. ?
I woke up at 11.40 in the night. ?
I often wake up in the night. ?

I can't solve this problem by consulting all my dictionaries though I have got tens of them. There are those phrases in them,but not sufficient sample sentences to show how they are used. Could you please help me? Thank you.

[albertino]

According to "Collins Cobuild-English Usage", we have the following definitions for the use of "night":
(1) Something that happens regularly during the night, i.e. the period of darkness of the day. For example,
The bat hunts for flying insects at night.
I used to lie on the grass to watch the stars at night.
(2) Something that happened during the night before the present day. So, you may say something happened in the night, last night or during the night.
For example,
I couldn't hear any chirping sound of a cricket in the night.
I had a nightmare last night.
I heard the dog bark from time to time during the night.
(3) If one is talking about a day in the past and one wants to say that something happened the night before that day, one can also say that it happened in the night, during the night or the previous night. For example,
Her mother had died in the night.
It was reported that an army of SWAT had parachuted to the desert to round up the terrorists.
The had climbed to the summit of Mount Everest the previous night.
(4) If one has mentioned an exact time and one wants to make it clear that is talking about the early part of the night rather than the morning, one adds at night. For example,
This happened at ten o'clock at night on our third day of travel.
(But if one is talking about a time after midnight and one wants to make it clear that one is talking about the night and not the afternoon, one says in the morning. For example, It was three o'clock in the morning.)

(Not a teacher)

[joham]

Oh, this is the perfect answer. How can I thank you enough!