The Scrum Master serves the Development Team by removing impediments to the Development Team's progress and facilitating Scrum events as requested or needed.

All events are time-boxed events, such that every event has a maximum duration. Once a Sprint begins, its duration is fixed and cannot be shortened or lengthened. The remaining events may end whenever the purpose of the event is achieved, ensuring an appropriate amount of time is spent without allowing waste in the process.

The highest priority of agility is to satisfy the customer through early and continuous delivery of valuable software. Because the Development Team is the one doing the work and increments must meet performance standards, they can expand their Definition of Done to include more stringent criteria for higher quality.

The Product Owner is also known as the value maximizer. He is responsible for maximizing the value of the work that the Development Team does. This is done through the ordering of the Product Backlog.

Many people misinterpret the Scrum Guide as stating the Development Team size is limited to 3-9 members. In reality, it only states that there is inherent risk attached to having less than 3 members and more than 9 members. As the number of members increases, the lines of communication also increase. This can be calculated using the Group intercommunication formula: n(n − 1) / 2 where n is the number of members. Some teams are able to handle the risk and "synergize" whereas others might struggle. Saying that, the relationship between defining a Sprint Goal and Development Team size is unclear.
But the relationship between the ordering of the Product Backlog, the PO having clear objectives, and the Sprint Goal are direct. The Product Owner typically comes to the Sprint Planning with a business objective in mind and Product Backlog items related to the business objective. After deciding what can be done for the upcoming Sprint, the Scrum Team will craft a Sprint Goal that would be met through the implementation of the items. This is not dependent on the size of the team nor length of the Sprint.
Scrum is also a framework that's fit for purpose. Some projects/products are not fit for Scrum... or, better stated, Scrum is not suitable for all projects/products.