Rules for preposition before time

Hi,

Rules for preposition before time:

1) We use no preposition with the following time expressions: this, that, last, next, tomorrow, yesterday, today, week

2) We use no preposition with time expressions that contain every, all, each, some, any and one.

3) “On” is used for days and dates. Example:

On Monday, on the Tuesday, on a Friday

On the 17^th, on 20^th, on a 18^th

4) “At” is used before night and precise clock. Example:

At 5 o’clock, at 5 pm

At night, at the midnight, at a night

5) “In” is used for months, year, century, and parts of a day. Example:

In January, in the July, in a December

In 1981, in the 90s

In early 20^th century, in the 19^th century

In evening, in early morning, in the noon, in an evening

I found this set of rules for preposition before time expression from the net. Are these rules correct?

If they are, then

1. “In the night” should have been “at the night”
2. “On one early morning in the 19^th” should have been “one early morning on the 19^th”
3. “Once upon a December” should have been “Once in a December”

By the way, is it grammatically correct to say “she wakes up at 1 a.m. in the morning” or should I replace the phrase “in the morning” with “in the night” or “at / on the night”

Thank you for your explanation.