"I am in", the way you heard it used, means "I will join you (in a given endeavour)", "I will participate (in the endeavour)", "you can count on me", "you can include me in your plans".
The opposite also exists, "I'm out". Meaning "I'm no longer participating", "I'm not onboard anymore".
It is informal, but that doesn't prevent it from being used in literature or movies to depict just that, informal situations. For example, in the movie Ocean's Eleven, George Clooney's character famously recruits Matt Damon's character by saying,
You're either in or you're out. Right now.
You can also ask people "who's in?" or "are you in?", etc. Again, this is okay for example for informal emails, but you won't see it used to invite people to a Royal gala, nor should you use it when replying to such an invitation.
Another common expression is "count me in", with the same meaning as "I'm in". (And the corresponding "count me out".)
The last usage of in is completely unrelated to all of the above. In that situation, in means "popular", "in fashion". (And once again, it is complemented by out meaning "out of fashion", "unpopular".) You can say, "red cars are in these days", for example. Or "gangsta rap is out". I would say this is less informal and more mainstream; you will find many newspapers or magazines, covering anything from fashion to politics, having a column titled "in and out [today/this week/this month]" or some such.
Oh, and if you still want to look these words up in a dictionary, look under "in (adverb)" and "in (adjective)" — not "in (preposition)" —, and the better ones will have the corresponding entry.
I don't believe that "for many times" is grammatical in any variety of English.
(Well, unless you contrive an example where "times" is the plural of "a given time of occurrence" and there's an elided "of the": "Class times are listed below. For many times, you can click the link for more information.")
You can use "for" with an ordinal: for the first time, for the 20th time, for the last time. Notice that it's always time, not times, in these examples. You can also use "for" with a duration: for 100 years, for the summer, for a long time.
"Many times" behaves the same way as "100 times" or "just a few times", and adding a "for" is not grammatical.
Mark has been to Hong Kong many times.
Mark has been in Hong Kong for two years now.
After Jessica failed 10000 times, she finally created a working robot.
After Jessica failed for the 10000th time, she tried a different approach.
Best Answer
There are a few alternatives here:
(ie. at most 1000 -- probably slightly less than 1000)
or
(ie. not just one thousand. The number of thousands is many.)
(ie. Because the number of species is many thousand ...)