LAN is the old name for LATAM, and though you have to be a bit careful on internal flights, broadly speaking you should get TPs and Avios for international services.
I know why you are asking about Z: it appears here:
http://www.britishairways.com/en-gb/...ing-avios.html
but not in the calculator under LAN, even if it is under TAM. This is awkward since in general the calculator uses the same database as the Avios awarding facility, so there is a strong chance you won't initially get Avios on Z (TPs I guess would be OK). However because of the link above I think you should get them if you persist since it's quite clearly OK there.
I would book via LATAM on the whole, however if you wanted a BA codeshare (for example) then there may be a case for doing it via BA, or if there was a complex trip involved. It won't make a difference to TPs/Avios. LATAM's computer system is makes BA's IT look good!