fingering is a very individual thing. Although some editor somewhere put down a certain fingering, it doesn't mean you have to do it that way. That said, there is something to be said for the conventional fingering -- 1 3 4 or 1 2 4 -- for the triplets, as it makes a it a little easier to put a very slight accent on the first note of the triplet on the first and fourth beats of the measure when needed. 5 (and occasionally 4), of course, is reserved for the melody, which must be distinct.
The whole thing must be legato, of course, and -- in my humble opinion -- is best learned without the pedal, although one should use the pedal once one has learned it.
In the left hand, to get a decent legato one really must use 4 and 5 (and even sometimes 3, if your hand is big enough), not just 5, on the octaves. Otherwise there is a very noticeable gap when changing from one to the next -- which you don't want.
As to what's written on the page -- once you settle on a fingering, there's no rule that says you can't write it in!