for the number one, looks like a statesman badge going to donate organs
the AMATI was to be LEXUS(toyota)/ACURA(honda) for the mazda, should have taken overtake the Eunos brand and replace it. Autozam (another mazda brand) was supposed to go ultra budget, so the low cost versions of mazdas were to be badged as that. middle range mazdas and top of the line Amati.
the Ẽfini started sort of similar to HDT(Holden Dealer Team), a couple dealers got together and desided to release own variations (top of the line with sporty motors)... quickly got backed up by factory and had few models
the above from what i learned the bellow are wikipedia:
Amati:
http://en.wikipedia.org/wiki/Mazda#Marques
Ẽfini:
http://en.wikipedia.org/wiki/%E1%BA%BCfini