Here is how I've answered these questions for my own game (because I feel my players will try some of this stuff during the playtest).
1.) How should combat maneuvers be resolved? Should they be modified attacks, a unique stat (something like CMB/CMD in Pathfinder), or some form of power/feat/ability?
A contest of attacker's Strength check versus the defender's Strength or Dexterity check, whichever is better. Except for disarm, which is a contest of attack rolls.
2.) Should they be limited to fighters, fightery-types, or open to all? If the latter, should fighters get bonuses to be the "best" at them?
Everyone can try it. At most, it could be a skill, "Brawling" or "Grappling" that is part of fightery backgrounds and possibly even a bonus skill from Fighter class (I think it's OK for classes to give a skill or two).
3.) Should they be part of an attack (do damage + trip) or replace the damage?
Replace. Damage+maneuver sounds like a good special ability, but for ordinary characters, KISS by just having a maneuver do an effect.
4.) How is the best way to resist the effects? Contests? Checks? Saving Throws? or something else?
It's a Strength or Dexterity saving throw, whichever is better, contested against the attacker's Strength check. This would seem to favor the defender, but remember that the attacker is the one choosing to use the special maneuver, and can choose to do it only when it favors them. The exception is disarm, which is a contest of attack rolls.
5.) Should they be a managed resource (you can use X combat maneuvers per day), be encounter-based (you can trip a foe once per encounter) or be spammable at-will?
"Wasting" an action and failing, when you could have been doing damage, is usually cost enough. But, if you use the same maneuver multiple times in an encounter, eventually the enemies catch on to your tricks and you get disadvantage on subsequent maneuver check.
-- 77IM