Question: I know there is no mining or harvesting on main map, but I was wondering about slime farms. Since (obviously) using utilities is cheating, what about using brute force, by creating a 5x5 room at each chunk, and seeing if slimes spawn? Of course, I'd fill up the unneeded rooms with smooth stone.
As long as it's legit, that's fine.
But keep in mind it's a huge gray area when it comes to deep-level tunnels and mining on the main map. Technically you can gather resources, so if you go slime-chunk hunting it really should be below ground you currently "own" (have a build on top of) and extra care should be taken not to overly-tear up areas you won't use.
But as long as you back fill the areas with stone you should be fine.
Also should be noted even if you find diamonds/ore down there you really shouldn't be collecting it unless it's reasonably in the way of your build. For example you can't branch mine and backfill the branches, but if you're making a slime-chunk grinder, you can grab the nearby diamonds/ores in the build site.
That's yet another gray area, really just falls under the honor rule, you can take ore that is reasonable and within your build area, but you can't "look for it".
semi-related note: Consider making a slime grinder in a swamp? That might actually have a higher output.