1. Yes, there is a path to becoming a partner but typically this would be as an Operating Partner and not on the investment side. If you want to transition you will have to do this earlier in your tenure in the operating team.
2. There is a very strong trend towards building up operating teams and most of the large PE funds are setting these ups. The reason for this is that cheap capital is chasing fewer deals so just using leverage to achieve returns is becoming increasingly difficult.
3. If you consider joining an operating team, make sure to look at the incentive scheme and how it compares with the investment team. This will give you a good idea of the standing of the operating team in the fund. If radically different I would consider my options.