So I'd like to have a connector to go through the case of my project such that I can disconnect auxiliary components when moving or whatever.

I need something in the 10+ pin range that can handle ~1.5A+ per pin.

I was looking at Molex's 'Microclasp' line, however, being this is my first time using such connectors, I am a bit confused. I understand that there is a female plastic piece that is then filled with crimped pins and connected to whatever. Then there is a male plastic piece that takes male crimp pins, and then connects to the female piece. However, looking at mouser for 10 pin connectors only female housings show up. If you sort all of the 'Microclasp' results by male gender, only the crimp pins and 2 and 3 pin housings show up.

Does this mean that mouser does not offer the male half of the connector for anything that is 4+ pins? Or am I misunderstanding the classification and/or terminology of the parts? For instance, is there a difference between a "receptacles", "sockets", and "headers"? Are all of those female housings, or are the "headers" the male housings? Which doesn't really matter in the case of the 10pin components offered by mouser, as both are listed as "receptacles" where one is a single row and the other two rows.

The microclasp are cable-to-board connectors -- not cable-to-cable. The cables are designed to have female connectors on both ends.

I think you'd be happier with a more standard connector like their "KK 254" line. The 2.54mm pitch is .1" and will fit a perfboard and standard pin headers with no fancy design required. If you want to make connectors that stick out the side of a project box you can just solder pin headers to a small scrap of perfboard and then screw that perfboard to the case.

I see. I think I'll go with what you suggested.

However, I'm still somewhat confused about the Microclasp connectors. If they are only female sockets, then what type of cable mates with them? A socket is rather useless without anything to go in it.

The female part is on the cable. You crimp the female pins to wires and then insert them into the connector housing. When complete the cable will have a female part on both ends. The male part is never designed for a cable -- there are no wires; the male receptacles are all designed to be soldered to a circuit board and already have the male pins molded into them.