using foreign key as primary key
Primary keys must be unique. As long as any particular user/user_id can't become more than a single seller/buyer (each), you will be fine. Whether or not that restriction does hold, depends on your domain. It would, e.g., fail, if a user can run multiple shops with each shop's owner being (considered) a distinct seller. (You might, e.g., want to attach contact information to a seller, which could be different from shop to shop - but specific to the seller, not to the shop. Just think of co-owned businesses…)
In case of doubt, you might want to play safe, and not make the foreign key the primary key to save you from the trouble of propagating a redesign through your schema some time in the future.

As for MySQL trying to attempt to fill in the gaps: If it is a foreign key, you(r application) will be the only one to insert records. Thus: No.