Here are a couple of housing sites:
香港房地產網|住宅放盤|物業按揭|搵 租樓 (then click the ENG link at the top for English)
Hong Kong Property, Apartments, Homes, Real Estate for Sale, rent and lease - Square Foot
You're going to be overwhelmed immediately as there are 10,000 lists in neighborhoods you've never heard of. Just to give you a starting idea, why don't you pick say Sheung Wan or Midlevels (both have a fair number of expats) and search for a 2br. That will give you an idea of some of the rates people are paying around there (and yes, it will go up to obscene numbers). Look at the size of the units (will be exaggerated a bit given the way they measure here) and then take a look at some areas like Kennedy Town or North Point on HK Island or Tsing Yi or Sha Tin out in Kowloon. You'll start to see how some of the prices / sizes differ in parts of the city. Look further out in the New Territories like Tai Po and get another idea.
Relocation packages are on the decline throughout most sectors. Some in the financial industry still have them, some do not. I'm not sure what the standard would be in the hospital sector, if at all.
Saying the air is better or worse in one part of town is kind of like saying "I have the best house in the worst neighborhood". When it blows down from China it's bad all over the city. That's is 200% of the WHO maximums in Central but only 150% in Sha Tin really isn't that much cause for excitement. My advice is if air pollution is a major issue (asthma, respiratory issues) don't come to Hong Kong.