The $3 coffee most certainly does entitle you to sit there for an hour. That's the whole point of getting a coffee in a coffee shop. And if you told me to leave after 5 to 10 minutes, I'd tell you to call the cops and make me. With that kind of attitude, however, your coffee shop won't be in business long, so it shouldn't really be a problem that you treat people with so much disrespect.
If they had signs stating their policy clearly upfront I would accept it, but if not, in the cultures that I know the purpose of a coffee shop is exactly to sit there for quite a while. I'm in Germany and I used to live in the US for a decade. If I go to a real Italian coffee shop (i.e. the owner is an Italian), of which there are quite a few, I see people sitting and chatting for long times, an hour is not unreasonable at all. They don't order much after the initial purchase either.
Also, the entire history of coffee shops is that they are places of meeting people, not vending places. So if a particular coffee shop wants to have a "10 minutes only" policy I'm certainly fine with it, everybody can lead their business as they wish, but to what I know this is against all expectations, so it should be stated right away.
For laptop policy it depends more on the local context and I would not always expect to see a sign if they don't want it, but just the acceptance of larger amounts of time spent sitting there alone is a more global thing I would think taht cannot be easily deduced just from looking at a place.
