I'd add a bit more solder on all joints. The pins get a lot of punishment when fitting and removing connectors, and can also get a bit of stress on them just from the connectors being pushed, pulled, etc. I make sure the entire pad is covered smoothly, and the solder travels a reasonable way up the pin.
Definitely, cut the key pins rather than removing them. The plastic base can twist and move without them. Probably not a big deal though, maybe not worth trying to get them back in there at this point.
Fully agree with Chris re J9 - looks like factory, but isn't! Cleaning away traces of flux is time consuming and not really necessary, but gives such a professional looking result.

Yep, that's been pretty warm there! Far more important to replace the loom connector than the pins though. If you use Trifurcon contacts, the burn won't happen again. Of course, if the pins on the board are damaged (burnt, corroded etc) you will certainly have to do those too.

With the Trifurcon, the center contact bears on a slightly different area than the single-contact pin, plus the two side contacts bear on fresh plating. As good practice, I do agree (and I usually do this when working on others' machines). However, in the real world, I've done only the loom connectors on my own machines when there's no obvious damage to the pins/board. They run stone cold (notably DE/sys11 GI, WPC GI).
I guess if I were replacing a single-contact pin with another, I'd replace the board connector as well because it will have suffered. But I'd never do that...
- if a pin is carrying enough current that it's having trouble coping, it's getting a Trifurcon. They're cheap.
- I always replace PCB headers with visibly compromised plating or burn (and I have VERY good eyesight for this particular purpose).

(Admittedly, part of the reason I'm even mentioning this is that the OP may need to get more soldering practice in, so removing connectors from boards unnecessarily may do more harm than good.)