You will never hear a native speaker use it in the context of the morning or afternoon. "Let's call it a night (or day)" means to stop something for the rest of the night (or day). A sample sentence: Let's play one more hand of cards and then let's call it a night. Interestingly, the original phrase was "call it half a day", first recorded in 1838, which referred to leaving one's place of employment before the work day was over.

Not really. There's no such common expression as "let's call it a morning".

No, not really. It's hard to make up your own idioms because a lot of them don't make much logical sense to begin with. :)

only if you are finishing something early and it is the morning or afternoon. Mostly used if you finish work early, or if working outside where you are subject to the weather. You can say "lets call it a day" if it rains and you can't work.

I actually think you could hear this in a work environment. A team is working on a project, with a certain objective for the morning. The leader says “We’ve finished everything we can this morning. Let’s go have lunch.” Or he could say “Let’s call it a morning”.