Hi @Laurent1990 , here are my best answers for you :)
1) I'm sure it will be. Cruises now dock close to PNG for tourists to visit, so I think if you did enough research and scouting around you'll probably find a boat to take you. That said, the immigration authorities in PNG need to know where, when and how you entered the country, so you may find taking a flight is easier on all accounts...
2) You essentially need to tell them when you are leaving the country. If this isn't possible with a return flight, you'll need a good reason as to why you are in PNG, and when you are likely to leave. PNG is quite a way behind other countries when it comes to immigration entry, so you'll need to keep things as simple and easy as possible.
3)Kokoda track - I'm an independent traveller too, but believe me when I say you'll probably have to do this with an experienced guide. Getting caught in the wrong place at the wrong time on the track could have pretty bad consequences. For anyone that does the trail, the PNG authorities want to ensure safety is your (and their) first priority. My suggestion is to find a local in PNG that has done the track several times and try and do it with them. If not, go with a group.
4) You'll love PNG. There aren't any places to avoid really, but like anywhere, be streetwise about where you are, especially in the evenings and at night, and especially in cities like Port Moresby. There is some tribal infighting in Hela Province, but other than that it's pretty safe. The people in PNG are incredibly friendly, and so long as you are respectful, they will welcome you with open arms. Try visiting the islands, Tufi Dive Resort as well as some of the highland regions - each area is unique in its own way!
Hope that helps!
Simon