How much of a bruising can a MTB take? I recently purchased my first MTB, a Rockrider 560, and I'm curious to know how much a roughing up can it take? 

For example, can I ride up and off kerbs without wrecking the tires? What about bunny hopping? Is that going to pummel the bike?

Tangentially related: My first ride with the bike (about 2 hours on off-road) was done without checking tyre pressure or if the new bike's chain was oiled properly. I take it this isn't going to have disastrouse consequences for the bike?
Assuming a decent and well maintained mountain bike it can handle much more abuse than riding up and down curbs or jumping around a bit. Even the most lightweight mountain bikes will not have the slightest problem with that.

However, two things are important: Good maintenance and riding technique! Riding on underinflated tires or a badly serviced suspension fork can easily lead to a flat or a bent rim when hitting hard on an edge. And good riding technique does not only make your riding look smoother but also is softer on your bike since it to some extent avoids the hardest impacts on your bike.

So go on with your riding, don't worry too much about how much your bike can handle, keep your bike well serviced and try to learn some decent riding technique.