ran for, ran after, and took all work in this sentence. In fact so does ran into but that is not what is being said here (that one is funny). The difference is their precise meaning. Note that the sentence is incorrect, it should read:
He __ the bus so he could reach the office in time.
1) He ran for the bus so he could reach the office in time.
This is the most reasonable answer and is appropriate for questions of this type. Using for implies there is a purpose to running, so you should follow it with something that justifies the action.
Examples:
He ran for the presidential office.
He ran for his own good.
2) He ran after the bus so he could reach the office in time.
He ran after shows an action taking place, use of after makes it sound like the man is chasing the bus, not merely getting it. This makes me think of the man actually trying to beat the bus to the bus stop.
Examples:
He ran after the ball and into the street.
He ran after the deer.
If there was a dog named Midnight, I would not say "He ran after Midnight." In this sentence, it sounds like midnight is a time. Instead, we would say "He ran for Midnight," just to avoid confusion.
3) He took the bus so he could reach the office in time.
This is plain and simple, and doesn't imply any need to run. The man simply took the bus.
Examples:
He took the plane to get to Shanghai.
He took the bag so that he would have books for class.
That is fine. Need in that sentence is used as a modal auxiliary and we use the bare infinitive1 after modal auxiliaries. It's called a 'semi-modal' because it can act as both a modal verb (like should, can, might, may) and a normal/lexical verb (as in She doesn't need to worry).
Try replacing the need with another modal auxiliary (for example should):
- She need not worry → she should not worry
(This is just for comparison and doesn't mean need not and should not are the same. This use of need not mean there's no obligation.)
It behaves the same as other modal auxiliaries and we always use the bare infinitive after them. However, unlike other modal auxiliaries, need is restricted to negatives and interrogatives.
- When the base form/infinitive is used without to, it's referred to as ‘bare infinitive’ as in I saw him dance (not *I saw him to dance)
Best Answer
Your second combined sentence is okay, though it doesn't exactly flow naturally. I'm not fond of keeping them all as separate questions either; it sounds like a barrage of questions you keep asking without giving anyone a chance to answer. ("Are we there yet? I'm bored, can I have a toy? I need the restroom, can we pull over? Are we there yet?"). A bit annoying.
I'd go for the middle ground and use two questions. This would flow easily, I think:
"Is she okay" is naturally distinct from the other questions. It isn't an offer for help; it's simply a yes or no question. So it seems naturally to separate it from the offers for help. (I think this is why your combined sentence didn't flow well.) You want to know if she's okay; you quickly follow that up by offering to help in two ways that pop into your head. Sounds perfectly reasonable to me.