The other version is a lot tinier, like eraser heads. You should be good with 3 then, like I mentioned. I’d still glance at the instructions just in case. At least this gives you an idea of how many you need.
Fermentation temperature can also cause a huge difference in taste. I'm guessing this last batch was a lot warmer due to the summer or do you control this in some way?
Carb drops came in different sizes. Coopers would be: 1 for 12oz, 2 for 22 oz, 3 of 1 liter (33oz). But there are some that are a lot smaller that take 3 - 5 for a 12 oz. Do you know what brand?
You cannot put them in your carry on (too many ounces (TSA rule)). But you can bring them in your checked luggage. I've brought rum back from Puerto Rico several times. State lines are OK.
Yes. Yes it does sound weird. there is no need to do that. adding something like that could actually do harm. Leave it be, the yeast are happy with what they've got.
Twist bottles can work... But the neck of the bottle is thinner and can snap off. They also have sealing problems. Why give yourself a chance to lose 12 oz of goodness like that?
Your next step would be a kit with steeping grains. Your LHBS or one of the major supplies have a ton of different kinds. But that would be the next move toward AG.
If you don't have hops yet, spray the leaves with dishsoap/water mixture. Most bugs won't touch the stuff. The only downside is that you need to reapply post rain storms.
Similiar to wine, I think there is a chance that there are some wild yeast strains that may be hitching a ride. I believe there is an additive added to grape juice before you add your yeast to kill any of the wild strains.
I wouldn't worry about not boiling the sugar. You might have some unevenly carbed bottles, but there are kits out there (Mr Beer) that uses straight non-boiled sugar. Was it optimal, no, will it likely work, yeah.
Moving your carboy around can cause some trapped CO2 to release and cause some of the trub from the bottom to float to the top. Rack below the stuff, give it a taste and call it good.