How Strong is my road bike?
Good question - I went down the same path (MTB -> road bike) and was worried about having to be super gentle. But actually, a road bike is surprisingly strong provided forces are applied in the right direction. Riding off curbs or over bumpy surfaces shouldn't cause a problem, but I wouldn't suggest doing drops. Similarily provided your bike isn't a super lightweight frame (and it sounds like it isn't) fitting a rack will probably be okay (especially if the frame has mounts for them). 

A lot of the pros on the Tour de France used their standard road bikes on the cobbled stages just with special tyres, and those stages were very bumpy. And the teams that used dedicated Paris-Roubaix style bikes mainly did so for comfort and speed, not strength.

It's when you start applying forces to the bikes in ways that weren't intended that you are likely to damage it - i.e. riding into things, jumps or crashing. That's where the extra durability of a mountain bike comes in. It also depends on your weight - without being rude, if you're a big rider simple physics means you are going to stress the bike more.

If you do do damage it may not be easy to see. Especially small cracks may be very had to spot, although if they get big they will be pretty obvious. I certainly wouldn't recommend assuming that just because you can't see problems there aren't any there - you really don't want your fork to fail at the crown which could cause a very serious accident.

If you are planning to ride your road bike off road a significant amount you might be better off with a cyclo cross bike. It will be a little bit heavier but stronger and more capable of dealing with crashes, but more importantly it will enable you to fit much wider tyres, and gives much better mud clearance. Many cyclocross bikes have rack mounts on them as well, and the geometry is tweaked to make them more comfortable to ride off road.

It's just my experience but as a mountain biker, I feel much more comfortable riding a cyclo cross bike - either on or off road - than I do a dedicated road bike, probably because the handling is better (for me).