For water supply in your basement, look into PEX tubing. If you're at all handy with plumbing, it's a great way to run temporary water. It's easy to work with, no soldering, and inexpensive - there's a crimping tool that can be $50-$100 but many big-box stores rent them. Or see if you can find anyone somewhat versed in DIY home repair that may know how to do it.
For drains, the nice thing about a darkroom is it's all sinks (vs. toilets and tubs which need plumbing run under the floor). If you have a floor drain, you may be able to run some PVC to it, or if your plumbing cleanout is accessible, you can take out the plug and screw in an adapter to run a drain pipe.
I made a big wash sink with an underbed plastic storage box and some drain parts and washers. $25 or so.
None of that would pass a code inspection, but you may not be into permanently altering your house for a darkroom - so temporary plumbing could be fine.
I'm amazed weekly at what's available on the used market - some beautiful gear's out there. It almost makes me sad... almost!