Phantomas21,
ICAO document 7300, a consolidated edition of the Convention on International Civil Aviation available from ICAO, answers your first question. Articles 54 & 57.
The Warsaw system of agreements addresses passenger, baggage and cargo liabilities. The principal instrument is the Convention for the Unification of Certain Rules relating to International Carriage by Air (Warsaw 1929) which has a number of amendments. A modern, but separate, agreement is the Convention for the Unification of Certain Rules for International Carriage by Air (Montreal 1999). You'll find more information on the ICAO Legal Affairs and External Relations Bureau
treaty collection page.
ICAO Annex 8, Part II, 3.2 requires that "a Certificate of Airworthiness shall be renewed or shall remain valid, subject to the laws of the State of Registry [...]"
Da-20 Monkey has addressed two of your three airspace classification questions. The summary table for ATS airspace classes (services provided and flight requirements) is in Annex 11, Appendix 4. The text of the ICAO standards is provided in Chapter 2. Be aware that the EASA ATPL air law syllabus mainly deals with ICAO standards, recommended practices and procedures. Contracting States may have established differences in respect of the classification and flight requirements of, and the provision of services in, their airspaces.
The third airspace question is unclear. Perhaps you'd reword it?
Your EASA ATPL theory provider is required to maintain a copy of the ICAO Annexes should you wish to pursue the details further. Additionally, EUROCONTROL's SKYbrary has published an invaluable
ICAO SARPS & PANS Search Centre where you can electronically search the Annexes and other ICAO documents.