No. He is president of the senate. President pro tempore is the title of the person standing in for him if he is not available.

He is technically the president of the senate, yes.

It is also ironic, no?

President of the Senate and President Pro Tempore of the Senate are two different positions. Pence is President of the Senate. Chuck Grassley of Iowa is President Pro Tempore of the Senate. That said, if the fraudulent Georgia senate elections are certified, some Dem senator will become President Pro Tempore of the Senate

Correct.

Correct

Yes

Yes you are correct, and he has been referred to as Mr President before.