Can I have my electricity supply split into two, so that I can have an independent meter in my outhouse, from my existing supply?
Probably not, but typically the utility will simply supply multiple drops for you. If you wanted to have two meters, the split would have to occur before the meters. Not many utility companies would be thrilled with this, as unmetered taps would be a major concern.
Also if you split the service, you'll be limited by the ampacity of the supply conductors. So if you pay for a 100 ampere service, you'll be limited to 100 amperes for both buildings. Whereas if you were to get two service drops, you could use 100 amperes in each location.
That depends on your local codes. Typically, however, your utility company will have to run a separate line to your other meter for your outbuilding.
If you are just wanting to run a power line from your existing setup to an outbuilding, then yes, you should be able to do so. Make sure that the breaker feeding that line is large enough to handle the expected load. Depending on materials used, you can run an overhead line, or a buried one. I prefer to run a line in pipe underground, just to avoid future issues.
Most code enforcement guys will be happy to go over what you need to do to stay in compliance. of course, then you will have to pull a permit and get inspected. Best of luck.