1. You should save the video files at the computer.

Question

2. We can videotape up to around 9 hours with the highest quality with the camcorder.
3. We are going to stay at a home for homestaying.
4. We'll leave Korea on Wednesday, January 23rd, 2007.

================================
Are the sentences all correct?

Answer 1

The first three are correct but awkward. They are not the way a native speaker would say it. The third sounds like a tautology, which is something that is obvious and conveys no information, like "A rose is a rose" . I don't know what you mean my "homestaying", by the way.
I would suggest the following improvements for the first three:
1. You should save the video files on the computer.
2. We can videotape up to about nine hours using the highest quality setting of the camcorder.
3. We are going to stay at a home during vacation.

Answer 2

DrWLS is correct about the first three sentences.

Sentence 4 needs one correction:
"We'll leave Korea on Wednesday, January 23, 2007."

It isn't correct to use the ordinal form of a number in a date when you include the year. Any of these are OK:

January 23
January 23rd
January 23, 2007
23 January 2007

=)