1. How much to get is largely based both on how much you have and how much typical lawsuits are. If you have no money and largely have no prospects for ever getting money, there's not really any need for umbrella insurance. Yes, future earnings can be gone after. As a doctor you're a nice target for something like that. Most lawsuits seem to be in the $1-$3 million range and settle for much less. Combining these two realities, getting a $2 million policy that sits on top of your auto and homeowner's/renter's insurance policies (which would give you around $2.5 million in coverage) would be a nice setup for where you are now, and you can always increase later for very little extra money. For example, increasing a $2 million policy to $3 million might only cost an extra $120 a year.
2. I shop this around. Currently I have all of my insurance policies with GEICO and I really like them. I'm also a Berkshire shareholder so I get an 8% discount. GEICO's prices and service are hard to beat.
3. Yes, you typically get discounts keeping all your insurance with the same insurer. Some insurers may not even want to write you an umbrellla policy if you don't have your auto and homeowner's/renters insurance with them. The reason here is that the umbrella policy sits on top of these policies so the umbrella insurer depends on the auto and homeowner's insurance to be well underwritten to minimize losses to the umbrella. Many insurers just feel better and more comfortable if they're in control of the whole process. Probably works out better for the client too. If you hit someone's Ferrari and give them back trouble you could easily get a judgement that eats into your umbrella. If you have this all with the one insurer you won't have to involve yourself with coordination between insurance companies.
4. Nope, you pay umbrella insurance annually, like you do auto and homeowner's. It's not like term life insurance where you lock in a lower rate for a long time. Things that would really boost your umbrella premiums are owning certain breeds of dogs that have histories of attacking people, owning power boats, owning ATV's, flying airplanes, stuff like that. These things will either hike your rates or you could get a lower rate by getting an exclusion, i.e. your umbrella covers everything EXCEPT your power boating.