I would like to know the usage of Jazakumu Allahu khairan wasalaam.
What is the appropriate answer to Jazakumu Allahu khairan wasalaam?
Do I reply Amin?
When is it best used and, is there any restrictions?
This is from the etiquette of a Muslim, instead of showing a small sign of gratitude, indeed it is better to make supplication for the person you are thanking, by asking Allah to reward the person with good.
Jazaa' - means reward kum/kumaa/kunna/etc. - is with regards to the person you are supplicating for, for example if it's a female: Jazaaki (the "ki" here is referring to "you" feminine), for a male it would be: Jazaka ("ka" for "you", masculine). For a group of people, or if you are speaking to someone of honor and respect i.e. a scholar: Jazakum ("Kum" = "you" plural).
Allahu khaira/khairan - All of this together becomes, "Jazaka Allahu khairan" - May Allah reward you with good.
Some people say "Jazak Allah", this would be wrong, because it could go either way, bad or good. Allah said in Surah Fussilat (v.28) "that is the reward of the enemies of Allah, Al-naar (hell-fire)..." Allah used "jazaa'" in this verse.
Or you can simply say, may Allah reward you, or elevate your status, etc. in English or any other language. This has no restrictions because it is a general du'aa and if you can't say it in Arabic, just say it in English.