Responses to your 1-3 in-line
I have heard that most consultants leave after like 2-5 years. Why is this usually the case? Can it be seen as negative when you stay longer than that?
Typical churn at BA (pre-MBA) or Associate (post-MBA) level is ~25%. Most BAs leave for an MBA. Most Associates leave to join a position in industry etc. This is due to a combination of (1) high-stress factors of the job (2) great exit opportunities (3) the itch to own / launch a P&L versus mostly advising on them. It is obviously not a negative if you stay longer; that's how you become a Partner.
Most likely (1) Internal strategy teams at firms like Google, etc. (2) Business Unit owners / GMs (3) Startup founders (4) Other consulting firms / niche firms.
Not sure I understand the question. There is an expected level of churn at these firms and the process is set up such that the juniors are not affected. As a junior you are also expected to be able to work with a different team-lead for new projects and you are, in most cases, assessed based purely on your performance at these projects, not on how "pally" you are with a team-lead etc.