I am getting ready to start a rocket stove for my shop based on Peter van den Berg's double barrel batch box heater https://batchrocket.eu/en/. I plan on using firebrick for the core.
I have no experience with firebrick or clay slip. From my research, it sounds like clay slip is the preferred material to hold the brick together.
This is how i made clay slip with dry clay. I bought Fire clay.
Fill a 5 gallon bucket about 1/3 full of water and than add a similar amount of Fire clay to the bucket. Wait over night or as long as possible before mixing. You are looking for something which your trowel can move through without it slumping. After the bucket has sat over night i poured the excess water off and started mixing it.
Wet clay will be different and need to be grated thru some 1/4 inch mesh with gloves on.
As for your second question. I believe you will either need to make something with refractory cement. Or look for larger bricks. Maybe ceramic fibre board would work. Kiln shelves. I am sure there are other options.
Note that clay slip is a leveler and sealer, not a glue. It does not adhere to bricks other than to make the surface dusty, and will not give structural support. You need to make sure your firebox is supported by other means, like rigid insulation backed with conventional masonry or cob.