This answer is based upon conclusions drawn from watching the movie(s) several times as well as references to certain Wookiepedia articles.
Given that Darth Maul's survival is built on EU canon, I will attempt to provide an answer within that level.
1. The Lightsaber
According to this article, Kenobi did not retrieve his lightsaber after Maul had kicked into the pit, he instead built a new identical one, as stated by this article.
However, since you mention the debate of whether he did in fact build a new one or simply retrieved the one from the pit, I will discuss this possibility briefly.
The pit is quite deep, exactly how deep does not matter right now, as Kenobi didn't have that information at hand at the time. Given this, I would think that IF Kenobi were to retrieve the lightsaber he would do it using, for lack of a better phrase, Force Telekinesis. Granted, he could not see the saber and had it been any other object, this may have proven impossible, but lightsabers are different: as is shown in Matthew Stover's Shatterpoint, jedis have a special bond to their lightsaber(s), going further than simply being a treasured tool (see below for more on this).
Thus, if Kenobi did retrieve his lightsaber from the pit, I would think it fair to assume that he did not venture down into the pit to find it, but simply retrieved it via Telekinesis.
2. The Pit
The Pit that Darth Maul falls into is in fact a melting pit and part of the Plasma Refinery Complex that serves as Main Power Generator to Theed. The Refinery drew a rare form of plasma from the Planet's core and refined it for use in powering the city as well as the starships of Naboo.
Given this, I draw these conclusions.
It might not even be possible to go down the pit, since it is in fact a melting pit. If so, they would have no reason nor any possibility to look for Maul's body.
If it is possible, which may be the case, they would most likely have to shut down the refinery plant for the duration of their investigation, which could leave a lot of Theed without power. If so, they probably considered it a wasted effort.
Since it was in fact a melting pit, they might simply have drawn the conclusion that between being split in half AND being thrown into a Plasma refinery Melting Pit, he could not have survived and there would not be much of a body to investigate. As you've rightly pointed out, the sith had been gone for a thousand years and as such it may not be foreseeable by the jedi that a person can survive being split in half by sheer force of will and hate (see this article, under "Defeat").
References other than linked
1. A quote from the book Shatterpoint, where Mace Windu reflects on his lightsaber, as a means to show the bond between a jedi and his lightsaber:
Because none of them understood what a lightsaber was.
Mace had begun the construction of his lightsaber when he was still a Padawan. On the
day he first put hand to metal, he had dreamed that lightsaber for
three years already: had imagined it so completely that it existed in
his mind, perfect in every detail. Its construction was not creation,
but actualization: he took mental reality and made it physical. The
thing of metal and gemstone, of particle beam and power cell, was only
an expression; his real lightsaber was the one that existed only in
the part of the Force Mace called his mind.
A lightsaber was not a weapon. Weapons might be taken, or destroyed. Weapons were unitary
entities. Many people even gave them names of their own. Mace would no
more give a name to his lightsaber than he would to his hand. He was
not the boy who first imagined its shape, forty-one years before; nor
was his lightsaber identical to that first image in the dreams of a
nine-year-old boy. With each new step in his ever-deepening
understanding of the Force and his place in it, he had rebuilt his
lightsaber. Remade it. It had grown along with him. His lightsaber
reflected all he knew. All he believed. All he was.