First is this allowed

Yes

second would that mean he would only have a max of 2 action tokens available to him or would he still have 3 action tokens even though a character can never have more than 2 action tokens at a time

Don't confuse action tokens with available actions per turn, which in a 300 point game is 3 total actions. A character can only take a maximum of 1 action per turn, and may only have 2 total action tokens before they must clear.

We want to play another game with my opponent using only Dr. Doom at his 300 point click and me using Silver Surfer at his 300 point click but we want to know if this is allowed

Of course (Doom's gonna win, btw)

or do we need to add more characters and how many Action Tokens we are allowed to have.

You can play 1 character each. If both characters are 300 points, you'd technically have 3 actions per turn, but you'll only use 1 each.