New slab draining and wall joining

[estmnt]

I am putting a new slab over an existing.

I dont need assistance in that regard, as I have successfully done it before. I need advice on how to best extend the drain, as seen in the attached picture. Also one side of the slab will be against the house wall (plastered brick). Would it be best practice to just use an expansion joint filler?

Please state your credentials when answering. Thank you very much!