i) Can a 3650 be stacked with different 3650 models ? ie) a WS-C3650-24PD-E (PoE) and a WS-C3650-24TD-S (non-PoE). Yes you can do it, (i did the same last low weeks) ii) no idea

kindly share sh run of asa as while network diagram along with IP details and which host connect which, also communication in which service (L4 port numbers).

dear Ken, Here you have to do Natting and define access list for that subnets which need to talk to domain, let me know if you need further assist.