Is there only a certain number of ores in minecraft per created map?

My question is above.

Or the ores will regenerate at a different place after a certain time. (I also ask mainly about diamonds)

There are only a limited number of blocks of a kind per map. The map is so huge that you'll almost never notice.

No, they do not regenerate. Once mined, there are no new ones. But since the Minecraft world is extremely large, there are more than enough resources.

No, it does not exist. There's a certain percentage (say 25-27%) that determines how much ore is present in the world. Since everything you do NOT see in a video game does not exist, the world will randomly generate when you're at the given height. So you can just leave it to luck if you find diamonds or not…