Why out of all the 613 mitvot was the para aduma chosen to be 'given' in Mara? 'Shom som lo 'chok' umishpat'. Chok refers to para aduma and why is it only mentioned so late in the torah after Korach. Its place should be somewhere in vayikra where other 'tumos' are mentioned.
Answer to Question 2
Rav Hirsch states on 20:19 that their were two main "Crown highways" leading through Edom. The first and most convenient road דרך המלך was the main high road leading through the valley where there were fields and vinyards and along which the wells were dug. That is why Moshe specified the condition "we will not pass through fields or vinyards or drink the water from the well, we will stick to the highroad and not turn aside to the right and the left:.
When this was refused, the messengers asked to be allowed to use the more difficult mountain route במסילה נעלה and to pay even for any water from the mountain stream along the route, even though it is normally free for all travelers.
Thus, Edom would not have to give thaem anything at all except permission to cross the land.
Rav Hirsch says on 20:22 that this is to emphasize that the death of Aharon was solely because of what happened at Kadesh with מי מריבה and it was his time to die. Thus he would have died at this point no matter what the response of Edom had been.
Answer to question 3
Rav Hirsch states that Moshe is to take the mateh in order to show that he is acting as the messenger of Hashem. However, hitting the rock with the mateh would imply that this is a special intervention from Hashem as a result of the uproar. Moshe is to take the staff "show them that you are still my messenger", but speak to the rock to show that it was Hashem who led them here and
... the required water was already provided by Hashem at the place to which He had directed them, and it mereley required a word from Moshe and Aharon to the rock which would suffice for it to produce the water which Hashem had placed ready for them
... without any fresh miracle, simply with a word from you, you are to provide them with a sufficiency for their undeniably present requirements.
This manner of obtaining the water would have convinced the people of the deep wrong they had done in accusing Moshe and Aharon of leading them to this waterless place against the will of Hashem; whereas water gushing fort only as a result of a blow could still leave room for the assumption that their having been led into the wilderness of Tzin wa originally a wilful arbitrary act on the part of Moshe and Aharon and only subsequently their justified revoltand their pressing need brought about the merciful miracle of Hashem.
Note that the first time in Beshalach he was instructed to hit the rock to show that this was an explicit miracle by Hashem just as the makos in Mitzraim or the splitting of the Yam Suf which also used the mateh.
Rabbi Sorotzkin in Oznayim Latorah states that the speaking actually was not to the rock but was to teach the Bnai Yisrael Torah and to raise their spiritual level to the point that they would have deserved the miracle of the water coming from the rock themselves (with no further action by Moshe). Moshe was to take the mateh as a "Plan B" only if Bnai Yisrael could not reach that level. The error was that he concluded that Bnai Yisrael could not be raised to that level and he required the explicit miracle of hitting the rock. This should have been delayed until after he had attempted to raise the Bnai Yisrael to that level.
Note that this also explains why Moshe Rabbeinu was instructed to hit the rock in Beshalach, since they were not yet at the higher level.