Is this sentence correct?
- Although I would like to start, nevertheless it is not possible.
Or should it be:
- Although I would like to start, it is not possible.
- I would like to start, nevertheless it is not possible.
Your example #1 is fine.
Consider this example from the 2002 CGEL, page 776, example [2.iii ], which is structured very similar to your example:
[2.iii ] Although he affects a gruff exterior in many instances, nevertheless he is fundamentally a man of warm heart and gentle disposition.
and their explanation:
Another very common case is represented in [2.iii ], where the connective adjunct has a reduplicative role: the relation between the main and subordinate clauses is already marked by although, so that nevertheless simply marks this relationship a second time.
ASIDE: As to your other two examples, example #2 is fine; but example #3 might be a bit controversial in that some people might see it as being a comma splice, and so they might expect or demand a semicolon or period or em dash to be used instead of a comma. Example #3 is okay to me for informal style, but if I'm writing in a very formal style or for a formal register then I might think twice before using a comma there like that.
NOTE: The 2002 CGEL is the 2002 reference grammar by Huddleston and Pullum (et al.), The Cambridge Grammar of the English Language.