I strongly recommend digging up and replacing the upper part of that underground clay pipe, down to the bend and the first joint, or, if not, excavating in order to inspect it and verify that it is not cracked or leaking at the bend (it probably is). Luckily, modern diamond cutters can cut clay pipe neatly for a new joint, without trying to patch it with concrete.
Most of the work will be in breaking out the concrete without causing additional damage to the clay pipe, but the hole will need to be big enough to stand in. Try to look down the hole to see how wet it is, and if there are bright red (sewage-eating) worms. It is best to dig out the wet mud and fill with shingle or crushed stone, which allows slight movement without cracking. You can top it with concrete, or slabs cut to fit (which will be easier to lift if you ever need to get at the drain again).
If you want to run waste pipes into the soil pipe, you could add a plastic gully with trap. This is little extra effort if done at the same time.
I don't favour using bitumen (sp.) paint on a wall. it will not stop water absorbed from below, and it will prevent evaporation from the surface, which helps it to dry. I think you will probably find the wet brickwork has perished and missing mortar, this can be hosed clean, and re-packed with mortar. You can use cement mortar underground, it is more durable, but if he feels it should have matching lime mortar, I won't argue.
An old wall built with lime mortar and soft bricks should not have cement render above the ground as it needs to "breathe" (lose damp by evaporation) which is also why it should not be bitumened.
Try not to be downhearted if the builder says you are being too finicky.