Do I have to play the Acts first before being able to play the expansion? I bought the expansion but when I create a new character, I cannot chose the Necromancer.

I was able to choose Necro from the start (Level one), but I’ve completed the game (before expansion) a ton of times already.

To answer your question, yes.

You may need to restart Steam or your PC, or reinstall the expansion. Necro should be available from level 1 regardless.

The new acts/areas are locked until you clear the base game. This applies for each difficulty individually.

You should be able to choose Necromancer or Inquisitor as your first mastery on a new character after levelling up once.