I am applying for a PhD, and trying to think about the future. While I am doing the PhD, would I be an employee of the University? Say, for example if I did Master's seminars - as was usual when I was doing mine - would I be paid? Are there ways of working part-time after the PhD and earning a salary? I am thinking about pensions etc.
thanks folks.

Depends on
1. What country you're studying in
2. Your subject area (arts, humanities, science etc)
3. Variations between different universities and departments.

No, you won't be an employee, unless they offer you some part time work (e.g. research assistant, tutor). The majority of full time PhD students in Australia are on a scholarship, which can sometimes include a 'top-up', either from the uni or industry. A PhD is just a qualification, and afterwards you will need to compete for a job with everyone else, unless you are offered a postdoc. Check out some other threads, where people have obtained their PhD, but are still looking for work 1-3 years later.