Say Autobot Cosmos has a Data Pad. Will Autobot Cosmos’s ability trigger if you draw the last card of your deck while he’s attacking?

Yes. Drawing the last card of your deck will cause you to shuffle your deck, and this will cause Autobot Cosmos to KO the defender.

Let's say I have Bombshell - Decepticon Psy Ops equipped with a Data Pad. When he attacks, would I trigger Data Pad's effect or Bombshell's skill first? Or do I get to choose the order they trigger in?

You may choose the order because they are both attack triggers on your cards.

If Dreadwing has two Force Fields equipped, wouldn't they both be scrapped at the same time? If a character would take 5 or more attack damage, both Force Fields would be triggered. Then you resolve them one at a time, in the order of your choice. The first one would scrap and reduce damage taken to 4. The second would scrap but the damage was already reduced to 4. This follows the Dinobot Sludge + Data Pad ruling where both effects are triggered at attack, and even if Data Pad puts your hand equal to your opponent, you still resolve Sludge's ability to draw 2 cards. Correct?

No. Force Field is not a triggered ability. See explanation regarding replacement effects above.

At what point does the upgrade I chose to move to Chop Shop take effect? During the attack so I gain the possible effect for my current attack, or does the cards effect (additional attack, additional bold, etc.) not happen until the next time I attack with Chop Shop?

You would get the benefits of the upgrade immediately, with the exception of abilities that trigger from Chop Shop attacking, because that event would have already passed (i.e. Data Pad).

Wave 2's Dinobot Sludge has a Data Pad. I have 2 cards in hand and my opponent has 3. When do I check for each to activate? Would I be able to draw a card with Data Pad, choose to not put a card on top of my deck (bringing my hand size to 3, equaling my opponent), and still draw 2 from Sludge's ability because when he attacked I met the prerequisites of having fewer cards.

Dinobot Sludge’s ability checks at the moment he attacks. This means both abilities will trigger at the same time, and both will happen. You can choose which ability to use first. If you use Data Pad’s ability first, and keep the card, you’ll still draw two cards from Sludge’s ability.