Why wasn't Gollum turned into a wraith?

[Landroval]

But still, I believe, hobbits were more resistant to temptation than Men, Elves and Maiar.

Yes; apparently, (at least) Frodo had the exact amount of power required:

Originally Posted by Letter #181

Frodo was in such a position: an apparently complete trap: a person of greater native power could probably never have resisted the Ring's lure to power so long; a person of less power could not hope to resist it in the final decision.

Why a Morgul wound brings about "more elvish" outlook is a mystery. There was some hint of translucency about the hobbit

Even the elves 'fade', due to the marring of Melkor and the consumation of their hroa by their fea.

Originally Posted by Aelfwine's preamble, Laws and customs of the eldar, Quendi and Eldar, HoME XI

As the weight of the years, with all their changes of desire and thought, gathers upon the spirit of the Eldar, so do the impulses and moods of their bodies change. This the Eldar mean when they speak of their spirits consuming them; and they say that ere Arda ends all the Eldalie on earth will have become as spirits invisible to mortal eyes, unless they will to be seen by some among Men into whose minds they may enter directly.

The letter is about a creature (Frodo/Aragorn/Gandalf/Galadriel) trying to withhold the Ring from Sauron in a direct confrontation. It is supposed that the person in question is wielding the One. Would he be able to beat Sauron?

Gordis, though you are correct in your clarification, you still owe us a proof that should Frodo master the ring, he wouldn't threaten Sauron.

Why would you want the nazgul to be more suspicious?

I doubt that at least the three great lords of Numenorean race didn't know who Sauron was; after all, at this time the numenoreans and Sauron were competitors in the race for middle-earth

He was universally trusted

No; in Lindon, the opposite was the case; and there were some, "few", of the other elves that heeded to the warnings about him.