It is daunting a shock and scary at first , One thing we do have is plenty of 'time' although some thing's can take 'time' they can be sorted even if they seem to take a fair bit of 'time' too sort out, Hopefully you should of been given some info at diagnosis even if after those words the world seems a total blur.
DVLA involves some form filling back n forth so contact them, while that is going on you should be able to continue to drive until a decision is reached, most get a 3 yr short period licence and your insurance shouldn't go up but you'll need to inform them.
Work is down to your personal circumstances, some carry on some struggle and some stop, you can claim esa or pip or both, or you can claim pip if your in work or not, it may also extend to your education ?. it would prob be best too find your local parkinsons advisor and make an appointment with them to explain all your options on work,education & benefits found here. http://www.parkinsons.org.uk/local-support
There are support groups nation wide some catering for working age people i'm 46 and one was recently formed in my area with around 30 members and some around the net 'young parkinson's network' springs to mind.
it may also be beneficial for you to get reff to your local parkinsons nurse by your neuro if you haven't already been so.
Any questions fire away