Learn English – what is the meaning of keep it up in this situation

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? Does she need any help, or someone to keep her company?

"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.

Typically the preceding 48 hours, which could refer to the current day if it is late enough. If someone said "the last two days" at 8 am, it would typically not be assumed that he was talking about the current day.