No idea what that is, though neither mold nor nicotine would have come to mind--it honestly looks more like splatters of dirt. We had similar speckles all over our house when we had it painted last year and they powerwashed the exterior--the old windows let all the splatter in and I hadn't thought to seal them off on the inside. I assume that type of scenario isn't in play here, though! To be clear, this wasn't there when you bought the house, but has since appeared? What have you already tried as far as cleaning it? If bleach or Simple Green or similar don't seem to have any effect and the mold guys don't think it's cause for concern, you could try covering it with a good primer to see if that hides it.

Thanks for input! The mold guy also thought it was odd but wasn't sure what it was--quite confident not mold though.

I noticed it very soon after we moved in. We haven't done any cleaning of it yet haha (wasn't sure if it was mold and a bigger project to deal with) , but we will now! Thanks so much!

When you paint, make sure you use a sealing bonding primer, and then paint the walls.

Could be who knows what got spattered on the drywall and later was painted over & has now bled thru the paint.

If it doesn't wash off completely, then you need to do as Cat suggested. BIN pigmented shellac (in the red & white can) is the tried & true product. BIN is alcohol based so you need good PPE and ventilation especially given this is a basement.

ETA: I don't think this is nicotine stains.

If you noticed it more or less when you moved in and haven't tried cleaning it yet, I think there's a pretty solid chance it will come off when you give it a good scrub. Could just have been something the old owners spilled as they were moving out and cleaning things (or maybe they did powerwash the exterior to get ready for sale--that's not uncommon in some areas--and somebody dropped the ball on noticing and cleaning this up). The smeared areas really don't look like either a mold growth pattern or something bleeding through old paint.

Oddly, I tried using magic eraser and other cleaners--these spots just will not come off! Well, at least I am not worried that it's mold anymore -- thanks for y'all's input, the mold guy agreed -- still super odd! He threw out maybe some sort of pest control substance used before? He really wasn't sure either but told me to clean an area and see if it comes back... .But I couldn't even get an area clean! lol

Something splattered. If the former owners were crafty, it could be a paint, some kind of glue, an oddball product, whatever. Paint over it.

The black on the particle board on the rafters looks like mold, but mold stains, so, often, long after the mold is dead, the black stain remains. A persistent leak might have caused the mold, the leak got fixed, the mold is dead, the stain remains. Make sure you don't have a moisture problem. It you don't, then it might just be an old stain.

Just here to cheer you on. As a former 1st time home buyer I remember the second guessing and worries! Take your time, prioritize projects that are safety related, and stick with it. Most home improvement projects don’t have to be done overnight. We’ve been in our place 10 years, and other than fixing broken stuff, hadn’t tackled remodeling until last fall. Once you get any pressing safety issues settled, take the time you need.

Thank you all not only for the input, but also for the positivity and encouragement.  It has been... A lot. Gas leak, 2 plumbing leaks differential settlement, leaking basement window, leaking foundation cracks.

BUT, it's ours and it's our home <3 my husband is all about aesthetics so it's coming together a bit too. Safety stuff first tho indeed!

And yes I think it's just remaining black stains and it seems the wood next to it was replaced? That's directly under our bed so I would be surprised if there's still an isolated water issue there. I got some mold spray for it

Or a waterbed leak?