IMO the "class picking" design you have laid out is flawed. It has been attempted many times in the past and has always failed. 1v1's in a tournament setting must start each round with a level playing field for both players. The nature of 1v1 is proving which player is stronger or more skilled. Giving an advantage like picking a class that counters another class is unbalancing the 1v1 before it even begins.
I would personally limit class picking to Scout or Soldier for the initial tournament. Based on results, you can expand class picking and rules for future tournaments but keep the first one simple.
Allowing players to "pick a map" can work but you need to have a specific list of maps that weed out bad MGE maps.
Each round is listed as "first to 10 kills" wins. That will make for an extremely short MGE match since you can get 10 kills on mostly any map in like 2 minutes? maybe 3?
If you want to keep everything simple, consider this example of a typical bracket matchup:
Contra vs SpaceCadet (Best of 3)
Round 1 - Contra picks class and map -- First to 20 Wins
Round 2 - SpaceCadet picks class and map -- First to 20 Wins
Round 3 (if necessary) - Player with most combined frags in rounds 1 & 2 picks class. Other player picks map. -- First to 20 wins.
Classes available to pick: Soldier or Scout
Maps available to pick: Develop a List
Having reserved servers is not a necessity. Both players could play their match on any available server as long as the match is complete before a certain period of time so it does not hold-up the rest of the tournament. All that should be required is a recorded demo from both players to submit if there is a dispute.