Yes, they need to keep him until they are at least ready to consider firing Brown. Otherwise they wind up in the same cycle of coach they won't fire with GM who doesn't get to run his team.
This is really year 1 for Monte right now.
Yep. However you feel about Monte's job performance, it doesn't matter at this point because you just let him hire a coach to a 4-year contract. What the Kings absolutely can't do is repeat the Vlade mistake, bring in a new GM, force him to keep Brown for a year or 2 and just waste another 5 years of this franchise.
A minimum 2 more seasons should not even be a question.