(1) which is correct

on vacatio or in vacation?

(2) when to use -- (hipen hipen) in english.

(1) On vacation (United States)
On holiday (UK and commonwealth countries)
Note that the GMAT, an American test written by an American corporation and used for admission to American schools, uses American idiomatic usage. If you've learned your English in a former commonwealth country, such as India, the differences can be very frustrating indeed.

(2) It's spelled "hyphen" (it took me a little while to figure out what that was supposed to say...).
You don't ever use two hyphens in a row. If you see two hyphens, it's going to be in a place where there's supposed to be a LONG DASH (a piece of punctuation that I don't think is supported by this forum). There are two main uses for long dashes:
* As a substitute for commas, in places where additional commas would be confusing. For instance:
I brought three of my best friends - Joey, Jonny, and Jimmy - to the club with me. In this sentence, putting commas where the dashes are would result in confusion, because there'd be a second possible reading (i.e., three of my best friends PLUS J, J, and J). With the dashes, it's absolutely clear that the three named individuals ARE the three friends.
* To set off a modifier that would normally be set off by commas, but which deserves extra emphasis because it is counterintuitive, ironic, or otherwise worthy of extra attention:
James - who had spent ten summers in the searing desert heat of Las Vegas - was constantly complaining that summers in Rhode Island were too hot. Notice that the content of the sentence is especially ironic given the modifier (we wouldn't expect someone from the desert to complain about New England summers, which aren't that hot), so we set the modifier off with dashes instead of the usual commas. Note also that this sentence wouldn't be wrong with commas instead of dashes, but it would lose a lot of its rhetorical force.

Is there a rule for what can be put after a long dash? Can I use the same rule for comma?
Thanks in advance.

try reading the immediately preceding post, which lays out guidelines for the use of the long dash(es). if there's anything in that post that you don't understand, or anything concerning the dash that's not addressed in the post, then go ahead and post another question.