The passive voice exists for a reason; as far as I can tell all languages have some way of creating a construction equivalent in semantics (and pragmatics) to the English passive.

At the semantic level, the passive voice operates on transitive verbs (=2 or more arguments; note that the subject is included as an argument) and "promotes" the transitive object to a subject. The meaning is equivalent semantically (barring idiomatic usages), as the subject of a passive construction is still the object of that transitive verb. Consider these two sentences below, where the event (=what happens to the object) is the same, in either active or passive voice.

1) John ate [the cake]

2) [The cake] was eaten (by John).

In either 1) or 2), this information is the same: there was a salient cake and it was eaten. However, note that the passive allows one to drop out the agent.

So, why would one use the passive voice over the active? Perhaps the writer/speaker wants to give attention to the object. In English the subject position is often where topics go, and so is considered the "important" element. Promoting the object to a subject via passive allows one to emphasize this. Another possible case: we simply don't know who the agent was or perhaps the agent doesn't really matter. The passive is also helpful for generalizing / avoiding assigning blame / being polite.

Consider these cases:

3) The trash can was blown over (by the wind).

4) John was really screwed.

5) That project got really messed up. (<= note how it doesn't blame anyone in particular)

In 3), it probably obvious what blew the trash can over (in general people don't go around blowing down trash cans, etc.). For 4), this begins to get idiomatic--we could try to attribute reason(s) why John is not in a good situation, but usually this is secondary to stressing that John is really screwed.

We can apply this reasoning to the example sentence you gave:

6) [Tonight's moon] can be seen from anywhere worldwide.

In this sentence, the fact that the moon is visible from anywhere in the world is being stressed, hence why the writer probably chose to use the passive. We really don't care who is seeing the moon.

You should use the passive when its the idiomatic way to talk about an event (e.g. the agent usually is implied or not important) or when you want to focus on the object of such an event, and therefore promote it to subject position via the passive construction.

1

I think the reason the book gives the answer stated in #1 is the subject of your question: passive construction of infinitive verbs. (I can't be sure because I don't have your book in front of me.) There are two verbs in the original sentence: "expects" and "to help." If the book asks you to convert the infinitive to the passive, then you need to change "to help" to "to be helped (by X)".

Note 1: "It is expected" is the proper way to make the passive form of "expect", but for whatever reason "It is expected by him" is rarely used. If you do use it, sounds better to my American ears to say "It is expected by him to be helped by me." However, the book answer is more natural at least in my northwestern American dialect.

Note 2: "It is expected that" is also very rarely used, and usually only in reference to a future event. If you do use a that-clause in this case you need to drop the "should" because it actually becomes a subjunctive construction: "It is expected by him that I help him." However, this should probably be avoided because this construction is so rarely seen.

2

"It is time for X" is simply the common idiom when the passive voice is used. Again, if you use that you need to drop the "should" and write "It is time that action be taken." However, it's far more common to see "it is time that" with a subject directly after, such as in "It is time that we take action." This wouldn't answer the book question correctly, though, since it asks for a passive construction.