Hey everyone, it's my first time posting, but I'm hoping somebody reads this and has an answer!

My family recently rented a new home: half of a side-by-side duplex, Foursquare style, about 1350 square feet, built in 1900. The house has been a buy neglected but still has a lot of the original charm, like original hardwood floors (downstairs) and unpainted wood trim in a red oak color that has darkened in many places with age (I at first thought it needed a good cleaning to get rid of the "darkened" areas until learning the value of an antiqued patina finish). While we are just renting, we will probably be here several years until I finish school and we can buy a house. Our landlord has gone "cheap" in areas of the house when doing repairs, disregarding the age and character of the home. Anyway, the upstairs doors are in a shameful state of disrepair and neglect (honestly, it almost put us off of renting, but luckily the wood in the rest of the house is in good condition. Actually the rest of the house, while nothing fancy, is quite nice and charming. Why they would keep up other areas but rent it with the bedroom doors looking like this is a mystery. This is the only major eyesore aside from the bubbling walls I noticed in our living room the other day, discovering that there was very old wallpaper underneath the paint!) The doors upstairs are similar to the trim but not with the noticeable grain, and a lighter orangey red vs mahogany red. They have the old ornate tarnished hinges, and old door knobs and locks. At first I thought they were original to the house, as the hardware is very old and all the doors still have the skeleton key holes. However, the doors are very thin and hollow. As you can see from the picture, no upkeep was ever done and the doors are all cracking and have the finish cracked and flaking off, with what almost looks like gray wood or paint underneath, but the graying isn't present under finish if you chip a fresh piece off. Our landlord likes to spend as little as possible and if we complain I'm sure he would either PAINT the doors, or replace with the new fake prepainted wood doors you buy at Home Depot (as he did with the bathroom door. The new white one sticks out like a sore thumb and the old door we discovered in the attic). What I'm asking is, how old ARE these doors? I would think around 1900 like the rest of the house, but I didn't think they even made hollow core doors back then. If they truly are that old though, rather than painting or replacing I would like to try my hand at sanding and then re-staining and covering with either poly, or amber shellac (which is on the trim all over the house). What would you guys do? Are the doors old and worth saving and refinishing? Or if I should just paint them, what color because white looks awful with cream walls and dark reddish toned wood trim. I'm attaching another photo to show how the rest of the trim that's in good shape looks.

You can too in this picture (from downstairs) that although in much better shape, the pocket door is a lighter color than the trim. The pocket door is like the "before" version of the upstairs bedroom doors...hollow, thin, 4 panel, and an "orangey-er" lighter finish than the trim, and unlike the grain of the trim the door seems smoother and almost like the ridges that are visible are from the stain rather than the wood.

Please help solve this mystery (how old are these atrocious doors?) and steer me in a direction. I may be renting, but I can't live with this eyesore and neglect for years. I don't mind putting the effort into refinishing, but should we just paint or ask the landlord to replace all together? Thanks!!!