Now keep in mind this is a old house with beat up old wood floors that are beyond refinishing.

If you have real wood floors and the urine staining isn't too deep sometimes you can sand slightly the top layer and refinish to get it out.

My question is: Is it easier to refinish/ paint the existing doors to have them go with our color scheme, or should we just buy new ones? 

New Roof, New AC/Furnace, 21 new regular windows, 6 new basement windows, 4 new metal doors, 16 x 66 blacktop driveway, new kitchen cabinets, sink, faucet, dishwasher, microwave and stove, new vanities, sinks and toilets in the bathroom, refinish hardwood floorsI'm pretty confident I can get $275,000 for it

The 10k gets me a new kitchen, hardwood floors refinished, paint, new bath.

So when you refinish the basement you'd have appx 3900-4k finished sq ft depending on how you do it. 

Wood refinished floors have huge gaps/cracks, and they are layed over what appears to be what was called a subfloor in the Victorian era, which is wood which also has gaps. 

All hardwood floors, which could be refinished.

:Up and Coming Duplex2 bed 1 bath unit that will rent for around $1600 (conservative estimate)1 bed 1 bath for $1000annual taxes 5kBeautiful street with walk to quaint shops and restaurants, should virtually 0 vacancy due to Portland rental market.Rent ready(new paint, solid appliances, refinished hardwood floors, mature low maintenance landscaping ) but could improve 1 bed unit for several thousand only.Will likely sell for around 450K+(similar property 6 months ago went for that, I offered 430K and missed out)Should I put in an offer and for how much?

The floor re-finisher I used let me help him with the work and so did my contractor buddy that did the windows.