Aussie seeking clarification (RoA among others)

Hi all, my primary aim is to:

• - be able to work without restricition within the EU.
  - obtain a EU permit/visa with the least possible amount of legwork (via my father..)

It seems the easiest way to do the above is via my Father: Born in UK 1949, he migrated to Australia in 1971 and married my Australian-born mother in 1973 in Australia.
I was born in 1974 in Australia and am an Australian citizen holding an Australian passport.
So far my research indicates all of the following are true:

• - I am (also technically) a British citizen in addition to being an Australian citizen by dint of Father's lineage. But did my British citizenship automatically expire at birth because I automatically became an Australian Citizen at birth in 1974? (both Australia + UK don't seem to have restrictions on dual-citizenship). Note my parents did not register me as a British citizen at birth.
  - I can pretty much apply for UK Citizenship + passport (noting the question above whether I am, at this time, a British Citizen), as well as RoA.
  - As soon as I get the RoA, I'm eligible to work as I please within the EU.

My specific questions are:

• - Am I a British citizen in addition to being an Australian citizen?
  - Is the RoA the best way to get unconditional right to work in the EU?
  - When applying for the RoA - Will the HO accept my Australian long-form birth certificate which clearly states my Father's DoB + place in the UK?
  - Can I just supply the long-form birth certificate to the HO and not have to supply any other documentation?

Let me know if I need to clarify any of the above - Dave

It seems that you are also automatically British by descent.
Proof of parents' marriage is also required.
Proof of father's British citizenship, etc.

Apply for a British passport if you also wish to work in the EEA.