I'm from Lund and can answer most questions about the city itself.
1.
Housing in Lund is not particularly cheap by Swedish standard but your sum should be enough. It's hard to get anything at all in august/september and january since the university semesters begin then and 35 000 or so students return to school. But almost every area is safe, close to your work and decent and therefore perhaps the most comfortable option.
Housing in Malmö is plentiful and cheap (by Swedish standards).
http://www.boplatssyd.se/Pages/Start.aspx is a website for public and private housing companies. The public flats goes to the ones who have queued the longest but perhaps it's possible to get a private flat directly if you have a decent income and a safe job (i.e. make a good impression). It's worth a try at least.
Otherwise there are many other private housing companies in Lund & Malmö which own apartments. Since i'm a mere student I would recommend you to ask around your potential job for advices there. I'd recommend centrum, västra innerstaden, möllevången, slottstaden and rörsjöstaden when it comes to neighbourhoods.
Blocket.se is the standard outlet for second-hand-apartments in all of Sweden if you only intend to stay a little while.
2.
Not sure but probably other posters have probably nailed this one.
3.
The public transportations are excellent. Train every 15 minutes or so between Malmö and Lund which takes about 10 minutes or so. 45 minutes by train from Lund to Copenhagen. Good transportations to other places in scania and Sweden. Lund is small and suited for walks or bicycles.
4.
English will work just fine. Especially in Lund which is an extremly international town with a large skilled expat community (i'm very crappy by student-in-lund-standards). There are english-speaking daycares and schools if you stay and have a baby but if you stay like 10 years or so, learning the native language is always a worthwhile investment.
Feel free to ask any questions at all. I know my city quite well. This post were written in a few minutes during a tv-break so some things may be a little messed up/hard to understand.
