Millionaro,
If you are flying private ops (eg hour building), your Class 2 medical if still valid will cover you. Class 1 only required for other than PVT ops. An appropriate person will have to hold a valid Australian rating if they are an instructor, will have to be operating under an AOC that permits international operations and you will have to get permission from the relevant national authority to conduct the "training" in their airspace.
Better to keep it PVT.
And unless you hold a foreign licence, certificate of validation or whatever the situation is, you may find yourself limited to VH registered aircraft as PIC as well.
Getting more difficult!
Lilfly,
If you are under instruction, the instructor, as PIC is the only one required to hold the current medical, eg ab-initio students, prior to 1st solo are not required to have a licence. Once they go solo (ie. PIC), must hold (and carry with them) the licence and medical.
Cheers!