It is, absollutelly, the project manager and the scrum master must work together to align all of the deliverables on the EDT to the product backlog and from there to the sprint backlogs.... task definition is the same, just have to prioritize them according to the PO and schedule them in sprints. Project management processes are almost the same, so are the scrum roles and practices.
Check PMBOK6 and it accompanying agile practice guide, released by PMI a few weeks ago.
It is. For this there are concepts like "Scrum of Scrum" and others.
Basically you just scale up the concept by taking one person per team and assign them to a higher level Scrum team as well, including a higher level Scrum Master. This Scrum of Scrum steers the project and can be even scaled further up by adding even more levels for huge projects.
This should be complemented by virtual teams across the existing scrum teams to foster knowledge transfer for particular topics like Q&A, architecture, or other important topics where learning and technical arrangements are crucial.
You can find a plethora of helpful texts and videos about how to scale Scrum if you search for it.
If you are interested, you can also check methodologies like LESS (Large Scale Scrum) and SAFe (Scaled Agile Framework), that apply agile techniques to large and complex projects and portfolio environments.
SCRUM is suitable for small team, less that 10, SCRUM of SCRUM is suitable for multiple team, less that 10 small teams (about 70 team members) for larger projects you could move for DAD, SAFe, LeSS. All the scalling Agile methods includes practices from SCRUM and involve extra practices to suit large organisation. For more info, please read this paper " A review of scaling Agile methods in large software developmet"
Normally UML and RUP are more structured and suitable for large IT projects, as addressed in all of the IT researches. If you want to use scrum anyway (which make sense) you can also take a look at the papers introducing the "hybrid methods" and try to overcome the drawbacks of Scrum by using another method on the side.