Sorry EllaKins. It is along drawn out subject that has been rehashed here for decades literally. Long story made short is that working for a franchise has many many benefits. But since they are independently owned and operated the actual working conditions can vary greatly, just the same as an independently owned ballroom studio. As long as any legal papers you are given you take to your lawyer to approve (as in ANY situation) then you should be fine.
It largely varies upon location. Like any franchised business, there are standardized business practices that must be followed by anyone that is employed or contracted by that studio. Ultimately though it is the business owner that will execute those policies, and either make it favorable or unfavorable.
If teaching ballroom and other partnered dances is your calling in life, starting out at Arthur Murray or even Fred Astaire isn't a terrible idea. Just keep in mind that you'll be expected to teach lessons after just a few months. It may be up to 6 or 12 months depending on the franchisee, but it can also be as little as 1-2 months if you have plenty of previous experience. Keep in mind that after this initial training, you'll mostly continue at your own studies either through their own coaches (which is encouraged more), or others.
Most teachers use them as a starting point because you can get certified relatively quickly through their system, which share equivalencies in various other certification programs. Arthur Murray is not known for paying their teachers well, even after doing a lot of pro-am entries. Most of them have high turnover rates just because once you have 2-3 years of experience, more money can easily be had at an independent studio or just being an independent teacher.
If you want to know more specifics, send me a PM. It seems like a lot of people are tired of the same discussions...