Yes, but he is extremely hard to catch and hidden deep in cerealean cave which you can only access after you have got all the kanto gym badges!
Yes, Mewtwo, Latios and Latias will be in HeartGold and SoulSilver.
mewtwo
Cerulean cave
Yes, you can. Pokemon HeartGold uses the time from your DS settings. So, change the time on the DS and the time in Pokemon HeartGold will change with it.
in curelen cave you get mewtwo
yes, in the cerulian cave
A level 70 mewtwo.
in cerulean cave at the end
You can't catch Mewtwo in Pokemon Diamond and pearl and also platinum. But you can catch Mewtwo in heartgold and soul silver
Pokemon HeartGold can communicate with all the DS Pokemon games. :c)
you dont you battle mewtwo and get out
You need to mate the Pokemon with a Ditto.