The questions are a bit too generic for any useful answers, but here you go:
1. It'd help to know details, such as life style, expectations, house/apartment etc. In the city proper, neighbourhoods in/close to the NE of KA are Rintheim (city-like living), Hagsfeld (pastoral), Waldstadt (heavily forested area sprinkled with tall apartment blocks, old bungalows and the odd mansion) and Oststadt (city-like). They're either within walking distance or with straightforward tram connections. Parts of Stutensee (Blankenloch, Buechig)(outside city limits) are also close by and well connected, if you prefer the more tranquil life out in the sticks. NW parts of the city are also nice to live in, but one would have to change trams to get to NE. By car this is not an issue.
There are also nice villages to the East, in a more hilly/forested area. maps.google.com and immobilienscout24.de are your friends.
2. All the English-speaking jobs are concentrated in the SW part of the city, and there's also an Office for English Jobs there. Kidding aside, it, again, depends on the field, qualifications etc. In IT there might be some. In Waldstadt there is a European School, but I think they're fully staffed for the year. If your partner is in pedagogy, it never hurts to ask, though.
3. ...I'm trying hard but can't think of anything. One tip would be to use the "search" functionality. :-)
4. Sorry to sound obvious, but probably the best place to buy a car would be a car dealership. There's more than 1 in the area, though, so you'll have to do some search: mobile.de, autoscout24.de, set your search criteria and restrict it to a small radius (kreis) around zip code (PLZ) 76133. BMW dealerships in the area are all part of the Ungeheuer holding (
www.ungeheuer.net).
2nd hand BMWs being cheap: I don't know, it depends. As a rule of thumb, big-engined gas cars depreciate far quicker than smaller-engined diesel ones. Rough numbers:
E36: from 2k EU to 8-9k. /6 (Z3s) range from 8k through 15k.
E39: from 5k to 17k, figure 10k for post-facelift models
E46: from 9k to 18k; you can find a loaded 330i with a few miles for approx 15k.
E60: from 17k to ...; early high mileage models are easy to find. You can find a fully loaded 545i with reasonable mileage for low 20k. Diesels are expensive.
E9x: from low 20k to ...
For older models, E30s, E31s, E32s are nigh on impossible to find. E34s are scarce. I don't know jack about Xs, but they seem to hold their value much better than non-X models. Figure low 30k for a run-of-the-mill old gen X5.
Cheers.