1)Why are the Jews letting the Plishtim dictate the terms of engagement? Why not simply attack if they believe it is the will of God?
The Jews has been unable to defeat the Plishtim (besides for Shimshon -- albeit on a microscale) for around 400 years. They had better technology (i.e. iron armor and chariots as evidenced by the posukim), and the "covenants" with the forefathers (from the midrash). Moreover, it is not a given that G-d's "favor" would have been with them in a pre-emptive strike in general. Furthermore, from a position of logic, if they "believed" that G-d was "with them" would it not be even easier to simply defeat 1 man (even if he was big)? This is actually exactly the position King David took, by referencing the fact that battle was indeed HaShem's, and that Golyath's provocation may have actually been the reason G-d's favor switched to the Israelite camp.
Besides for the above, King David having previously been anointed King, need a way to become famous. This episode provided a way for him to upstage the current leader and begin that process. This is similar to how Hashem had elders forget (an) element(s) from their Torah knowledge in order for Hillel haZaken to become well-known in his time.
2)Would they have been halachically bound, had they lost? Could they have ignored the whole thing and still attacked? It would seem from the simple reading of the verses not, but why not?
It seems that the issue of desecrating G-d's name would have likely obligated them to fulfill their declarations in an open covenant especially if it was agreed upon by a halachic King.
3)If they couldn't find anyone for several days, why didn't they either decline and propose and alternative or else why didn't the Plishtim count it as a forfeit?
As stated above the episode serves as a way for King David to become famous and begin his fated ascension to the throne. For the sake of argument, it is likely the Plishtim did not want open war with Saul's newly formed empire, fresh off their defeat of Nachash, King of Ammon. By displaying their best warrior and having no one want to fight, it was a way to shame the entire nation and their new King, and additionaly through Golyath's actions, desecrate G-d's name. The Israelites never formally declined, thus the Plishtim were able to continue on with their shaming etc. possibly creating defavor in the eyes of the nation.