Apple gives a free upgrade to Mountain Lion if a new Mac is purchased in a nearby time frame.
I got a redemption code.
Will I be able to download Mountain Lion again next time, for example in two months from now, will I need it?
Once you have purchased something in the App Store, you can always download it again without paying (This is the same on the Mac App Store and iOS). You will see it in your 'purchases' tab in the Mac App Store.
So once you use your redemption code, you have 'purchased' it, and can install it whenever you need it.
Yes, it just appears in "Purchases" tab of Mac app store so you can download it on any mac computer until you use the same Apple Id