The countryside consists of the hilliest bits, which the government and developers pretend that they can't build on (Don't look here or there at the hilltops with towering apartment blocks perched on them, it'll spoil your suspension of disbelief) and the flat spots which the government hasn't yet chosen to build a "new town" (i.e. insta-city) on and which tend to be non-trivial to reach since mass transit hasn't been extended that far since the government hasn't yet chosen to build a "new town" there since...

What's happened is that a small number of wealthy families have basically completely captured HK and "real estate" accounts for a huge chunk of the local economy. HK residents and, increasingly, PRC citizens seeking a way to smuggle ill-gotten money out of the PRC proper park their money in the form of tiny cement apartments which they have no particular need to rent out to anyone since there's a prolonged property tax holiday in effect.

The value of tiny cement apartments only stays high so long as there's the appearance of scarcity of tiny cement apartments. This requires the apparent scarcity of land.

The Hong Kong we tend to think of is the very densely populated Hong Kong Island and Kowloon area across the bay. Actually there is a huge area beyond Kowloon to the north known as the New Territories which is much less developed:

http://en.wikipedia.org/wiki/New_Territories

Less than 25% of the total land area of HK (~400 sq. mi.) is developed.[1]

[1] http://www.gov.hk/en/about/abouthk/facts.htm

Open google map and turn on the satellite mode. You will see there are lots of green areas in Hong Kong.

Most of Hong Kong is undeveloped land (and a lot of that is undeveloped because it is protected national park). This is why you end up with such high density despite so much land with only 7 million people.

Yes and some nice beaches too.

Lots of it.