How many cards do I flip if my opponent shuffles their deck while attacking Omega Supreme (Spaceship)–triggering Combination–and I have Evasive Maneuvers on Omega Supreme (Spaceship) and Urban Camo on Omega Supreme (Base)?

When you combine into Captain Omega Supreme, you get to keep 1 upgrade in each slot, so you can keep both Evasive Maneuvers and Urban Camo. You’ll flip a total of 6 Battle Cards. After the battle, you’ll scrap Evasive Maneuvers.

If Cerebros attacks and, using his flip condition, fetches a Grenade Launcher from the scrap, what happens to it?

The Grenade Launcher will be scrapped after battle. This is in contrast to Fusion Borer, which would stay on Cerebros after the attack. This is due to a change in language as the game evolved. Early on, WotC used language like "After the upgraded character attacks -> Scrap this card.". Later, they adjusted to "When the upgraded character attacks/defends -> Scrap this card after the battle.". This newer language ties the scrap to the more common "When battles" trigger and not to the rarely used "After battle" trigger". The same is true for other older cards like Evasive Maneuvers, Blast Shield, and Power Punch, vs newer cards like Emergency Barricade and Crystal of Power.