Cut and paste this link to the K&N website - installation guide for the Terrano, with pics - its a doddle.
http://www.kandn.com/instructions/57-0125_inst.pdf
As to exact HP I couldn't tell you, but their main pages will have something useful I'm sure.
All I can tell you is it definitely gave the 2mpg fuel economy improvement, and since it was an auto box it was easy to assess performance improvement in terms of the lower frequency with which the box had to change down at the same given speed on some regular hilly journeys, so definitely a bit more oomph as well.
And no, despite much advice to the contrary, I didn't disconnect the battery for 24 hours either!
If you want to be picky, you might hear a little bit more air sucking when you give it welly, but other than that its a no-brainer and easy as pie to fit.
And as I say, despite all the scepticism, I've driven through some serious flooding at times with water washing over the bonnet with no effect whatsoever. As I always used to say, its how you drive the thing that counts - as for its height in the engine bay, well the electrics will get drowned before the filter does!
Similarly with criticism about hot air under the bonnet (the standard box gets its air from a constricted pipe into the inner wing) - at normal pace theres a Force 9 gale blowing into the underbonnet area, its only when you stop that the engine bay heats up significantly.
Its the 57i kit you need - JFDI I'd say, it works great for me and has done for 110k miles so far, just about to fit the same to my recently-acquired 02-plater. Good luck!