After finishing the story, can I replay the acts with the same character?

Let's say I want to replay the game with the same character , can I ? At the end, does a new game starts automaticly at a higher difficulty or can I play at the same one ?

The Story is always the same difficulty. So act1 areas will always have very low level monsters.

A character that has completed the quests will not be able to do them again, but all the monsters will be there if you want to kill them.

Being higher level than the story monsters will impose an XP and loot drop penalty to you.

There is so much end-game content to do...

But if you want to do the story/quests again, just roll another toon. Half the fun of the game is seeing how the different builds play. (Very differently...)