You will find many abandoned buildings, feel free to repair them and use as outposts but I'd recommend you build your own place as a main base.

Branches are free wood just break saplings instead you can punch them.

Yes you do want to build your base near water, boats will become your primary form of transport and will likely be where your refinery is unless you intend on building multiple bases on other islands.

You are already dead so you will not starve, need sleep or to drink water, doing anything like this will just give a temporary boost in stats but it isn't required to survive.