Each embassy sets their own requirements. So what someone else used might not work for you. You need to contact the embassy you applied through and ask them as they are the ones who are deciding what they will accept.
You can still apply for a single entry tourist visa, but you no longer send in your passport. It's all done online, and your visa is an e-mail that you receive with a document you print off.
But currently visa exempt has been increased to 60 days and you can apply one time for a 30 day extension. So not applying for a visa will give you the same amount of days as if you do apply for a visa at the moment.
You need to ask the embassy you will be applying through. Each embassy sets their own requirements so what someone else experienced may not be the same thing you will experience.
Yes, it's possible to do it yourself. But you will still have to find and pay for the boat trip across. Probably won't have much issue with that as there should be some around aware of why you are there and ready to assist.
you don't need any insurance before applying. The application specifically says you can leave the insurance section blank and then fill it in after your provisional approval before you get your full approval letter when you choose how you want to pickup your visa.