In this following sentence:
Shall I say:
I hope he dies
Instead of saying :I hope she will die.
Besides, shall I say: "I hope she is cooking at 8." Instead of "I hope she will be cooking at 8"
Thanks so much!
After the verb hope you can use any of the many ways to refer to future time, including
I hope she cooks at 8
I hope she's cooking at 8
I hope she will cook at 8
I hope she's going to cook at 8
I hope she'll be cooking at 8
I hope she's about to cook at 8
I hope she's to cook at 8
The simple present can be used for future events seen as in evitable or following a timetable. "The train arrives at 8 o'clock". or "We all die". The same meaning could be given as "will arrive" or "will die" but the sense of certainty is lost.
This is still permitted with "hope". It is quite natural to use it with something widely seen as inevitable "I hope he dies". The second sentence could be phrased "is cooking" or "will be cooking", with almost no difference in meaning, though the first does suggest she is following a timetable or a plan.:
We need to have everything ready for the party at 1pm, so I hope she's in the kitchen and cooking by 8am, otherwise the turkey won't have time to rest before carving.