It seems as though answers to some of these questions can be found in the novelization. This FAQ deals with questions in the movie's continuity. It's always possible that George Lucas will create new material for Episode II and III which contradicts information in the TPM novelization. For this reason questions in the FAQ are not answered with the novelization. Currently, there are plans to create an Appendix in this FAQ which deals with what the novelization has to offer.

A.  How come Yoda and Mace Windu did not detect the dark presence of Chancellor Palpatine at Qui-Gon's funeral?

"Hard to see, the dark side is." -Yoda
Considering how many times Jedi and Sith seem to foresee and sense things, it's still very strange.

In Episode II: Attack of the Clones, we find out the Jedi's ability to use the Force has diminished, and Yoda mentions that the Dark Lord of the Sith is the only one that has that knowledge.

The Dark Side of the Force doesn't follow all the same rules as the Light. Darth Sidious is the Chancellor of the Republic and no one knows it. He can obviously camouflage his intentions.

B.  Who sent a transmission from Tatooine, giving the Sith a signal to trace?

C.  What "revenge" do the Sith want on the Jedi?