Impossible to tell with absolute certainty from a photo, but the brown staining is most likely from creosote. Creosote deposits on the interior of the chimney seep through the porous brick and mortar, especially when rain water enters the chimney. This staining is very difficult to remove because it permeates the brick. It's not just on the surface. This kind of staining does not happen with a properly lined chimney. Perhaps a liner was added after years of use without one. No "certified" chimney would be unlined today.

Several things..the island will feel less contrived if you were to replace the table with a round. The current square brings too much attention to the angle of the island. Either replace the foyer wallpaper or re-do the wainscoting to match the two—tones in the d.r. If you decide to replace the foyer paper be aware of background white/off-white/creme, etc. when choosing your paint color. I agree new fans without lights is in order. I think once you have all elements in place then would be a good time to reselect your lighting. Lighting has a huge influence on the overall look you are trying to achieve. Your home is lovely and has a very nice lived-in look. Good job!

I'd like to say 100 years is old- a house from last turn of the century is old. But just a year span isn't really the whole definition for me. I often call a house old if it was built without indoor plumbing or electric- like an urban house from the 30's can be old, or some more rural homes into the 40's can be old. Houses built without ventilation in the walls for heating or cooling usually gets called old by me too, lol. Older homes for me usually run in between the 40's-80'sish. Has built in plumbing, electric, and ventilation in the walls. Modern kicks in late 80's-2010ish. Has plumbing, electric, ventilation in the walls. Usually has "model home" or "McMansion" sorts of vibes with built in kitchens and the start of using stone for counters. New or newer is around 10 years old- though that can vary a bit too by a few years. If it still has it's original parts and working good, that's newer. If stuff like roofs and flooring needs replacing already, that is not so new anymore.

Is your attic finished, or do you have only boards over the floor joists. Homes of this age can be balloon construction, meaning you could drop a line from the attic and it would go through to basement level. I'm not a pro, but looked into foam injected (via outside) for a mid century home and was told that if foam was used, it would fill up wall cavities, making access to future electrical work very difficult. I opted for blown in cellulose by a highly reputable company who filled all voids to avoid heat loss, and installed a sealing attic entry door with vertical sides to preclude movement of cellulose. You might want to look at some DR. ENERGY videos before deciding on best type of insulation.