Вам нравится прочитать темы о космонавтике?
Нам нужно ... , назначать время, чтобы ...
Я размышляю: разве они обнаруживают нас?
Kevin think of Russian verbs as of two-for-one things.
We have perfective and imperfective aspects of verbs.
Perfective conveys that the action happens once, or that it has happened and became or will become completed/finished.
Imperfective means that the action is ongoing or repeating, the English equivalents are use to, would, keep doing, and the simple tenses like "I clean the floor myself", "I got up early when I was young", which imply the habitual order of things...

So that:
"Вам нравится прочитать" sounds like "you like to finish reading"
(perfective doesn't work because "прочитать" means "to be done reading" as opposed to the right option "читать", the corresponding ongoing action)

"нам нужно назначать" sounds like "we have to keep on setting up"
(imperfective doesn't work because you have to set up a time only once, should be perfective)

"разве они обнаруживают нас" sounds like "if they go on finding us out"
(should've been perfective because they are supposed to have discovered us only once)

Something like that.

Lena gave all the right answers, compare and analyze.

My best wishes!