* Would AE and FN have been able to write any notes while they were stranded? Would they have had paper and pencil with them?
I presume so. Fred would have needed pencil and paper for his calculations, at a minimum. AE was an author and kept some kind of journals or diaries.
If so, when the realized their end was near, would they have put these notes in some kind of a "safe" place ?
That depends on many unspecifiable factors. How sharp were their minds at that time? Were they in denial about the fact that they were about to die? Did they have their pencils and papers close at hand at all times?
* Would they have tried to make some form of more or less permanent inscription(s) on some hard surface? Tree, rock...?
I mean wouldn't they have tried to leave some form of recognizable trace of their presence?
If they left such permanent inscriptions on Niku, TIGHAR hasn't found them yet.
Even if they did leave such inscriptions, people or natural events may have removed them. The destructive power of wind and waves is astonishing. There was a rather large marker at the end of the landing channel when TIGHAR began to work on Niku; it is gone now.