I've never had to fix anything this tiny, but for assembling miniatures for boardgames and for fixing a couple figures, I've had success with medium consistency model glue (fairly thin stuff like superglue, not a thick adhesive). I got a small bottle for like $3 at Hobby Lobby and a little bit goes a long way just like with super glue. You just need to make sure you only apply a little bit so that it doesn't make a mess. It will adhere just fine to painted surfaces but it will also make a mess if you let it smear/run on painted surfaces (as in it will leave glue film, not like it dissolves the paint).
Fixing Aigis' accessory may be difficult because of how it's shaped and how small it is but I'm sure it would work for the fin-hand on the second picture since it has a small peg you could dab a little bit of glue on.
Stuff I've had success using it on:
Assembling the
entire Super Dungeon Explorer miniatures set. Not my picture but you can get the idea. I don't have mine painted but I did assemble them all and some of the joints are very small (weapons, hands, etc.).
Fixing a scale figure's broken base. Figure has metal peg in foot, plastic base actually had a small piece crack off so the figure couldn't stand up. A dab of glue fixed the base and now the figure stands good as new.
Nendoroid petite hand that kept popping out. Since they're not able to be posed to the extent that real nendos are (hand not designed to turn at the wrist, in this case), I just glued it in.
I can't remember what it was (I think it was a nendo) but I know there was something else where I had a situation like what you mention on the Amatsukaze's turret's fin and I got tired of the piece popping out so I just used a tiny dot of glue to put an end to that.