The large horizontal black object that is tubular is an iron core wire wound inductor, most likely for the woofer, you can just see the red coated magnet wire of the inductor peeking out on the right side top of the picture. There are two air core inductors on white bobbins at slight angles to each other on the left side of the crossover. At the bottom, it does indeed look like there is some type of blue edge connector but I am not familiar with how Fried did his crossovers to confirm this. I don't see any particular screw mountings though on the the circuit board so you might be able to rock it gently side to side to see if it comes loose.
But very importantly, you should be tracing the wires to each driver and label each with polarity or terminal (driver and wire) so that you know EXACTLY how they wire back up, pics here will also help.
I know you've recapped crossovers before, it's just a reminder. Been there, done that (or forgot to do that), got the T-shirt.
Plenty of NP electrolytics on there, I suspect the yellow Seacor film caps are likely Mylar polyester caps. For most of us, the recommendation is to change like for like types. There are those who suggest changing out Electrolytics for film IF the sizes allow and fit, would be an interesting exercise to do one side with electrolytics and the other side with films where possible and then see how they sound.
Lots of discussion on that issue.