While in bot mode, Sunstorm's attack is equal to number of cards in hand. If he is equipped with a Mining Pick and you start with, let's say 6 cards in hand when the attack is initiated. You Plan 2, dropping 2 from your hand to the top of your deck, bringing you down to 4 cards in-hand with a plus-4 total from the Mining Pick, for a total of 8 attack before battle flips? Or would it check for the 6, giving you your base attack, then you can Plan from there, starting you with a base of 10 in the same aforementioned situation. I guess my question is, when does his ability check for cards in hand? The second he is tapped then go on from there? Or at the end of battle flips then check hand size and calculate from there?

Sunstorm’s attack is always checking your hand size, so the damage he does in an attack comes at the very end of the attack.

Does Blurr’s ability combine with Mining Pick to allow you to plan 2 again on the attack of the untapped character to get +5?

Yes.

I have a Torox with Tooth and Claw and Mining Pick in his Armor Slot, as well as Divebomb with a Field Communicator. If I combine them into Predaking via the Predacon Enigma, am I required to keep Tooth and Claw in order to carry the Mining Pick to Predaking's armor slot, or can I bring the Field Communicator instead?

Once an Upgrade is legally put into a slot, it stays there, even if the ability that allowed it to be upgraded in the first place no longer applies. In your example, you could keep Mining Pick in Predaking’s Armor slot. Upgrades that are on characters that combine into Combiners are considered to stay in their slots, even though those slots now belong to the Combiner.