Let's meet in the morning or at the morning.
in the afternoon or at the afternoon.
in the night or at the night.
in the park or at the park.
working in the background or at the background.
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Let's take them one at a time:
Let's meet [in or at] the (morning or afternoon).
This is to meet at a general time in the next (most immediate) morning. "In" is the correct choice. The resolution applies to both 'morning' and 'afternoon,' as each refers to a non-specific time frame.
Let's meet [in or at] the night.
"The" here is where one might trip. For someone proposing a clandestine effort, to say "Let's meet in the night" is arguably plausible if uncommon. More conventionally, however, one would say "Let's meet at night," with no need to use the definite article "the," as each day has only one night.
Let's meet [in or at] the park.
You can make a valid case for either preposition. The park is a specific location when seen on a map, but any location within the park is also "in" the park.
working (in or at) the background
In most contexts, foreground and background are an abstract, relative relationship, not a fixed point, thus making it difficult to rationalize "at." If you have, for example, three layers, the middle is in the foreground relative to the rear-most layer, but in the background relative to the nearest layer. Also, since "working" implies a use of the word "background" in a notional sense of a secondary process or task, not a specific place, I would almost always recommend "in" as the correct choice.
Where is Tia's father? - "He's in Tia's school" It's not routine, he does not do anything there regularly. But now...
Where is Tia? - "She's at school" Talks about her routine engagement, daily activity of not just being there, but also study.
There are two questions in this!
Let's take the first one.
When we talk about a 'point of time' it's generally 'at'. And thus, we see the following examples:
at 8 o'clock
at midnight (this means 0000 hr)
at noon (1200 hr)... and so on
But when we talk about the 'period', we are not sure 'at what particular point of time' and thus, we see these examples:
in morning/evening/night etc.
However, we do find 'at night', but then I think it's used for a regular happening and not for that very night. Say...
The mother always tells story to her kid at night - talking about an 'every-night' activity
Do you remember, her murder happened in the night - not a routine, of course!
Nevertheless, 'at night' was used even for non-routine things, but years back, I think.
Actually, 'in school' is common in AmE and 'at school' in BrE.
If I talk about InE I practice,
I'd generally use 'at' simply to show 'presence'.
Where is Tia's father? ~ "He's at Tia's school"
It's not routine, he does not do anything there regularly. But now...
Where is Tia? ~ "She's in school"
Talks about her routine engagement, daily activity of not just being there, but also study.
In India, you quite frequently hear someone asking --
Which school she's in? and never 'at'.
I could not get what 'background' you are talking about. But more or less, the latter piece of my answer shall address it.