I expect that you finish by 5pm - correct, but not common usage.
I expect you finish by 5 pm. - incorrect. See the next sentence.
I expect you to finish by 5pm. -----> is the preposition "to" fundamental? "To" is required, and this is perfect. In this case, 5 PM has not happened yet. Also, this sentence is more of a command, rather than an expectation.
I expected you finished by 5pm. 5 PM has passed, but you need to add "to" and use the present tense of "finished." So: "I expected you to finish by 5 PM.
I expect that you'll finish the work by 5 pm. Also good. In this sentence, the writer is confident that the work will be finished.
we expect that our employer pay us a reasonable salary. Again, using "that" is not common usage.
we expect our employer to pay us a reasonable salary. -----> is the preposition "to" fundamental? And yes, "to" is necessary.
we expect our employer pay us. Add "to" before "pay" to make it correct.
we expect to receive money from/by our employer. "From" should be used here.
I expect it to rain ------→ I don’t understand the construction of this sentence.
You can say, "I (subject) expect (verb) rain (noun/object). For your sentence: "I (subject) expect (verb) it (object: think of the sky - while not exactly true, it's a good way to visualize "it") to rain (infinitive verb).
I expect that it will rain. correct
I expect raining tonight. incorrect
I expect to work until 9pm. correct
I expect working until 9pm. incorrect
I expect to eat pasta tonight. correct
I expect eating pasta tonight. incorrect.
I expect a positive answer from/by her. "From" is correct.
A general note: Newspapers sometimes drop words like "to" so that a title will fit on the page. Also, it might be easier for you to read answers in the NOTEBOOK section. It allows teachers to highlight words, etc.
Hope this helps. :-)