I have a head ache. It lasts 3 days, so I'm going to the hospital this morning.

I have a head ache. It lasts 3 days, so I'm going to the hospital this morning.I have a headache. It has lasted (or I have had it) for 3 days, so I'm going to the hospital this morning.

Let's move on today's homework :)

OK.

I beilieve that ghosts exist.believe

She knows me.

OK

I like tea.

OK

I want to watch the fireworks tonight.

OK

I neet to some rest.I need some rest.or I need to get some rest.

The country is longing for a strong president.

OK

※I have no idea, the word of long.

Sorry, I don't understand this.

Of course I knew, it's long, or the pencil's long or something like that, So far this is OK.but I'm not famililer with using above.I don't understand this. Sorry.

He smiled at me.

OK

I'm in the school now.You probably mean: "I'm at the school now" or "I'm at school now".If you are a student, then you need "at school"; if you are visiting you need "at the school".

This is correct but not a likely sentence: "in the school" could only refer to being inside the building. If you are a student and are there for school then you need to say "at school".

The party will be held on August fourth.More often you will hear: "on the 4th of August". What you wrote is correct, however.

OK in UK English. I don't know if it's correct in the US.

Prease read the novel from the beginning to the end.

OK

That's all.

OK

There are simple words today too, but I learn a lot from those words!

This might be correct, but without a context I can't be sure.