Stains on curtains and grease stains wallpaper near upper cookstove

[oxblood]

We have brown ring-shaped spots on our curtains only in the living room / dinette & kitchen sink areas of our 2003 Airstream classic Limited 34'. These came off fairly well with Resolve Upholstery cleaner and soft damp sponge. What caused this? Mold? Mildew? Grease? How do we prevent this in the future? Any better methods of prevention or treatment would be appreciated! We priced new curtains with A/S - cost $3,600.00.

When we store our Airstream for 6 months or so (in Texas) under covered RV parking, should we crack a window, or leave the Fantastic fans on low? Would ventilation help us with these issues?

Also we have stains around the vinyl wallpaper behind the stovetop that are not coming off with 409 and a brush or sponge. We presume these are grease stains. Any suggestions? Thanks and happy travels from Austin, Texas!!