Welcome to Permies Linda!
The heat riser doesn't necessarily have to be built from thin fire brick. It could be a perlite/clay mix, ceramic fiber board, vermiculite board etc... If you do use the fire brick though (which is fine) it is thin (vs the full bricks) for a few reasons: 1) As the firebrick needs to be insulated, the thickness of the chimney needs to be kept to a minimum to maintain a good gap between the barrel and the heat riser and not cause a bottleneck in the flow of the downward traveling gasses. 2) The firebrick tends to rob heat from the fire when cold and takes longer for the stove to get up to temperature but has the advantage of maintaining warm for a longer period of time so the next startup is much easier with a good draft. Also, a thick full brick would take roughly twice as long to heat up.
The manifold doesn't reach super hot temperatures so an ordinary mortar
should hold up but I don't have first hand
experience with this. If you were to use a clay slip as your mortar it would be no problem for sure.