I would avoid using litter box liners with rabbits. Mainly because they will likely chew them, and the absorbent material that is often in these liners, not to mention plastic in general are very dangerous for a bun to ingest. I would be using litter in the box, I use wood pellet litter (sold as wood stove pellets, horse stall bedding, or cat litter), many people also use compressed paper pellets or carefresh, but I find the wood pellets more economical and much better at odour control.
The cardboard borders are safe
Some rabbits like to shred cardboard which is fine, however if they ingest a lot of it at one time it can lead to blockages, so just keep an eye out for that.
The door on the house will be fine, you could have certainly made it smaller but it won’t be too big. I prefer to make the doors on my cardboard houses a little on the small side because then my bunnies love adjusting them to their desired dimensions 