Q1 - yes the flight must depart from, and arrive at, a designated customs airport.
Q2 - General Declarations (effectively a list of everyone on board on a small aircraft, plus nationality and passport details, and a declaration that no-one on board is ill), a cargo manifest, plus all the standard aircraft documentation like Certificate of Airworthiness, Certificate of Registration, Certificate of Insurance etc.
Q3 - flight plans are relatively straightforward, as Australia has adopted the ICAO format. Manifests and customs declarations are best prepared by someone who is familiar with the process.
The larger issues are obtaining overflight and landing permissions (varies from country to country) and the issue of import duty. I have an acquaintance who is associated with one of the main service clubs (Rotary) and they no longer send stuff to PNG because it is inevitably hit with duty (even for used items) and someone (usually several people) in the chain have their hand out for a bribe.
If you do manage to overcome all that, the next problem you will encounter is that there is no Avgas in these countries.
A noble ambition, but unfortunately the practical limitations make this un-do-able.