Your questions cannot be answered simply, Craig. They raise a whole lot more questions, the first being "what regulatory environment? FAA? EASA? Other?"
EASA for example, requires a commercial operator to have a Continuing Airworthiness Management Organization (CAMO) with a "nominated postholder" responsible for managing it. The CAMO must include a person responsible for the quality system, with direct access to the accountable manager (usually the CEO). The operator's quality system is extended to the contracted maintenance organization. The maintenance and quality systems are an AOC responsibility that cannot be delegated, to an MRO or anyone else. This means that although producing the maintenance schedule can be contracted to an MRO, responsibility for its content and the managerial oversight of compliance with it, cannot be delegated.
So...
1. Generally speaking, you can split up check packages pretty much as you please, as long as all maintenance is accomplished within the approved maintenance intervals. The Boeing MPD provides recommendations, but drawing up a maintenance schedule from it and getting the schedule approved is the operator's responsibility. The operating environment determines the actual intervals - e.g high cyle/short sectors or low cycle/long sectors?
2. MROs are commercial businesses and any MRO will run whatever maintenance programme the customer desires. They aren't responsible for producing it - although they will if you pay them cold, hard cash. Responsibility for getting its content approved by the regulator remains with the AOC holder.