I was a Gates-Cambridge finalist in this last cycle. There’s no fixed formula for getting invited for an interview, let alone getting the actual scholarship. All of the students I met were extremely driven and were committed to benefiting the world. There was very little ego and even though we were ostensibly competitors, there was absolutely no hostility. Everyone was genuinely interested in helping and learning from each other. If you have the stats to perk your department’s interest and you have the drive and commitment to help others, then you have a real shot, though, for even the most brilliant and wonderful people, there’s nothing close to a guarantee.
One of the major problems that you’re facing is your goal of a getting a masters scholarship as an international student. Masters are seen as income sources by universities, so it’s incredibly difficult to secure any funding, especially as an international student, where you don’t have access to a large portion of the total funds. The wisest move for you would be to apply broadly both within and without the university. Don’t expect any funding and have a backup plan. Good luck!