Yes. Definately get rid of the asbestos first. This will be very messy, including damping down the area. Not something that you'd want to subject your new hobby room to. There was a large thread on this subject
click here for details. The way I understand it, you can remove the stuff yourself (taking adequate precautions), bag it up, label it, and take it down your local tip. But do check with your local council first. They will have a designated site to take it.
Chances are, if it's an asbestos roof, the support structure is going to be inadequate for anything more substantial. It would probably be best to put a completely new roof on. which type of roof you opt for depends on the existing structure, your own taste/budget etc.. If you want further advise on this please give details of the sheds dimentions, and shape. Is it a pent roof (has it's highest point running down the middle), or is it just a single slope.
Drylining consists of laying plastic sheets up the wall. Fixing battons to the wall on top of these, and then fixing plasterboard to the battons. While you're at it, you can, optionally, put insulation between the battons before you apply the plasterboard.
How to tell if you already have a damp proof membrane in the base is more tricky, as there are so many ways of building a shed. A Damp Proof membrane is simply a large plastic sheet set into the concrete a few inches below the surface. If your brickwork starts lower than the floor level inside the shed, chances are, you have one.
If your brickwork starts at the same level as the floor inside the shed look for the raw edge of the plastic sheet sticking out the sides of the base (probably a few inches lower than the floor level). If after carefull inspection you can't find it, chances are you haven't got one.
My advice would be to sort out the roof first, followed by laying a DPC and screeding over the floor (if required) next, and then do the Electrics and dry lining. Replacing doors, and windows is another whole subject, and you may also want to fit some ventilation dependant on the windows you select to keep/install.
As this is post takes in so many issues it would be worth your while to concentrate on one area at a time and post more specific queries based on those areas.
Blimy have I typed that much already
. Hope I havn't bored you to tears.