The coolant is supposed to last like 7 years. The procedure is simply to draw and refill. I wouldn't flush it with anything unless you have a very good reason to it. It's difficult to get 100% of fluid out of the system so you're gonna end up with more diluted coolant than you want due to...
It's the connector for the wastegate actuator. I can't see what's broken from your pic but if its functioning correctly still just heatshrink over it or wrap in electrical tape if you're concerned about water ingress.
I'm sure if the cat was easy to remove it would have been gone too. I guess there's a benefit to having it integrated into the downpipe lol.
It's very fast if you know what you're doing. We actually had them on security footage, but nothing usable. he was in and out in about 2 minutes.
It's a shame CSF doesn't have an option for the 10th gen Civic yet. If I ever need to switch mine out on the STi I'd go with their aluminum rad that has a thermostatted water/oil cooler built in. That's a really elegant OEM+ option to this problem.
Just to double check, are you sure you're not getting stumped by the immobilizer? If you disconnect battery power you need to hold the clutch AND brake to the floor to get it to start, otherwise it'll do the crank/rumble/die thing like you're describing.
A friend of mine here is a mechanic who has done this numerous times.
I think the only major issue is there's some subtle wiring differences depending on the year and trim of car. It's definitely doable.