Yes, they do. You can select adjustable or fixed corner posts.
The answer to this one depends on what door size you've gone for and what size the corner posts end up being. We recommend using our 3D Planner to identify the answer as it will automatically calculate the space for you. Also, take a look at our help pages for additional info.
Integrated appliances do not require housings. Just leave a gap equal to the width of your integrated appliance, plus 2-3mm extra, and slide the appliance in when you fit.