building the rocket mass heater

I have two questions   1) Why does the heat riser have to be built using the thin fire brick  & 2.) if I build the manifold using clay brick can I use an ordinary type S or N mortar

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.

1) the split bricks are usually used in the heat riser so that you can then use insulating fire blanket around the riser to offset the temperature difference between the inside and outside of the riser. It is a matter of volume--if you use the full bricks, they will not insulate as well, and when wrapped with insulation blanket does not leave much room within the barrel for the air to move. It is a matter of permformance--the splits with blanket will create a stronger stove.

2) Don't use premade mortars--they contain cement and will disintegrate under the extreme temperatures. Use clay slip to bond the bricks--I recommend using Fireclay--or use refractory cement which is good up to 2400F.

And if you haven't purchased "the book" yet, I suggest purchasing a copy.

https://www.amazon.com/Rocket-Heater-Builders-Guide-Step/dp/0865718237/ref=asc_df_0865718237/?tag=hyprod-20&linkCode=df0&hvadid=312111910505&hvpos=1o1&hvnetw=g&hvrand=10230949885155598450&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9021394&hvtargid=pla-434338542873&psc=1

Erica's "Heat Riser Cookbook"

https://permies.com/t/84432f7/Heat-Riser-Cookbook

Erica's big gob of plans, including a bunch of different risers:

https://permies.com/t/40993f7/Ernie-Erica-Wisner-Rocket-Mass


Erica's plans for the cob style rocket mass heater in DVD 1 of the new 4-DVD set - in the log structure (wofati)

https://permies.com/t/110333f7/Homestead-inch-Rocket-Mass-Heater