If it's rust, a drop of Whink (brown bottle; you can find it at a supermarket, target or walmart) would dissolve it almost on contact. I've had good luck removing old blood stains with straight peroxide. But with either of these two products, you HAVE to rinse like mad, and that could make the fabric discolor or bleed. So probably the first thing you have to do is take a clean white cloth, wet it, then go over each part of the color in the material to see if there's any dye transfer. If there is, you'd be best getting someone to come and clean it for you. Both Wink and peroxide are some of the more extreme methods of cleaning. I'd probably start with something a little simpler (like a paste of Biz) before I went for the drastic stuff. And as always, you should try any stain remover stuff on a hidden area to see if it discolors the fabric or causes damage. The other thing re: steam is that steam can SET a stain, esp. the marks around the edges. I know from personal experience on a stain on an upholstered wingchair.

you don't say what the fiber is, but as a former sales rep for cpt mills, most cpts have some built in stain resistance so trying to add something on top of it is sort of risky. Since your walking on the fiber and its always 'crushing' and rebounding topical treatments are seldom as effective as treatments of the yarn itself before the carpet is tufted.

This could be nictotine gathering in humidity of the bathroom, or it could be latex in the paint. Both have been proven to have this result. You can get a mop and see if it comes off with some Pinesol or sugar soap, then wait for it to fully dry, before putting on a coat of Kilz or Zinzzer mould killing primer. To stop mould growing back, you could try a full white vinegar on the mop after you have cleaned it, and before priming.

Buy better quality varpet that has it built into the fibers. Aftermarket is a rip off, as it’s removed after every cleaning and needs to be reapplied. And it atttacts dirt and makes it wear out prematurely due to that.