It’s awesome that you are trying your best to care for the bunny
There’s a BUNNY INFO section on this site that you could read – it contains a lot of useful information on bunny care!
As for your question, I think it really depends on the individual bunny. There are some bunnies who are generally more relaxed and less jumpy, while others get spooked by the slightest sound. If Richard has a personality that is laid-back then it should be quite normal. That being said, rabbits are quite known to hide their illnesses as a result of being a prey animal, but Richard sounds like he will be fine
How big is the cage? Bunnies do need a lot of out-of-cage time (an hour or two is actually quite little) so if he’s trying to escape it may mean that he is getting bored being in the cage.You mentioned that your dog gets to roam the rest of the house – does this mean that it’s not usually in the living room? If that’s the case you might want to consider letting Richard free roam in the living room.