Did you put those periods at the beginnings of those sentences on purpose?
We must hurry; the guests should/ought to come for another hour. No. Incomprehensible. What are you trying to say?
．The weather should/ought to improve after the weekend. Good.
．Kate should/ought to be here soon--she left home at six. Good.
．She has been studying hard. She should/ought to do well on the exam. Good.
May I ask how do we negate those sentences using "should/ought to"? Do we simply use "shouldn't/ought not to"? No. These are problematic. Like:
．We needn't get ready yet; the guests shouldn't/ought not to come for another hour. the guests probably won't be here for another hour. they aren't likely to be here for another hour.
．The weather shouldn't/ought not to improve after the weekend. probably won't improve until after the weekend. is not likely to improve even after the weekend
．Kate shouldn't/ought not to be here soon--she missed the bus. probably won't be here. is not likely to be here.
．She has been very lazy on her schoolwork. She shouldn't/ought not to do well on the exam. probably won't do well. is not likely to do well
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These negations present a great many problems. This use of shouldn't (ought not to) has to do with what you think is not likely. ought not to is even more rare than shouldn't in this meaning. This non-expectation meaning is easily confused with the meaning It is not advisable that ....
You can say things like this:
We've been waiting for hours, so it shouldn't be long before Sally finally arrives. (probably won't be long)
And even:
She's very understanding, so she shouldn't mind if we borrow her umbrella for a while. (probably won't mind)
But this second one is already shading into expressing an opinion that she is somewhat obligated not to mind if we borrow the umbrella.
And last (one of yours):
Kate shouldn't be here soon. This one means, quite clearly to me, It is not advisable for Kate to be here soon, or Kate must not be here soon, or Kate had better not be here soon, or It's not a good idea for Kate to be here soon. With soon it's especially anomalous. It doesn't mean what you were hoping it would mean.
CJ