Is there a penalty to doing so and if so what? Do your city centre improvements periodically get damaged and how bad is that if so?
There is no penalty for settling on one type of tile of vs another. There are varying stats and bonuses for the different tile types but no penalties.
Building on top of a resource will give you access to that resource. See here for example.
Some tile types are favored more than others, such as plains hills, as your city will start with 2 hammers 2 food.
More information on this thread if you're curious.