Will the 575 mb fit in a 605 case?
It might
fit, but it won't be a drop in replacement. There would be a load of hackery involved.
Here's an LC575 motherboard, with a PDS card:
The white edge connector at the top goes into a slot which connects to the internal wiring harness. It has all of the connections from the mobo to the rest of the machine - power, SCSI, floppy, front panel controls, speakers and video. External back panel connections are at the bottom.
This is the slot it goes into, and part of the wiring harness:
Here's a Quadra 605/LC475 motherboard, in its case, and a clearer shot of an earlier LC pizzabox series motherboard:
As you can (kind of) see, there is no edge connector, and thus no wiring harness. Instead, it uses standard, separate motherboard connectors for everything internal.
Adapting a 575 motherboard to a stand-alone machine should in theory be possible, but you would need to strip the wiring harness out of the 575 and adapt it to your choice of case. It would not be a trivial job at all.
There is a breakout adapter for external Mac video, but they're not easy to find these days. Try ebay seller olde-mac-milt.