YES - For a cross-border flight, you can contact your country's European Consumer Centre. For a domestic flight, contact a national consumer centre in your country.
YES - and the cost of each item (the fare, taxes, charges, surcharges and fees) must be clearly displayed.
YES - provided your air carrier is licensed in a European country.
NO - as you did not comply with the requirement to present yourself for check-in within the time stipulated.
This depends on national law in each European country and will therefore vary throughout the EU.
If the delay to the first flight was within the control of the airline, then you are entitled to compensation for denied boarding on the connecting flight.