The only part of your question that can be answered is the last one.

The earliest mention of the name Zeus – di-we or di-wo – is in Mycenaean Linear B tablets of the Late Bronze Age (e.g. KH Gq 5), mostly dating to the 13th century BC. As Oliver Dickinson puts it in his The Aegean Bronze Age (1994), "Some names are recorded at more than one site, not only well-known names such as Zeus, Hera, Poseidon and Hermaias (Hermes), who might well be among the greater gods of the Mycenaean world, but figures unknown or totally obscure later such as Diwia, Marineus and Ko-ma-we-te-ja (Komawenteia?)" (p. 291).

There is even a reference to a "Diktaian Zeus" in the tablets KN Fp 1 + 31. Mount Dikte is where, according to later Greek mythology (e.g. Hesiod), Zeus was born.

But whether this early Zeus was similar to the one familiar from later Greek mythology (i.e. from Homer onwards) is a question we cannot answer. There are, for example, no images from the Aegean Bronze Age that are similar to later depictions of Zeus (e.g. a mature, bearded man brandishing thunder bolts). As Susan Guettel Cole writes, about Dionysus but the same applies to any of the Olympian gods encountered in the Linear B tablets, "we have no idea what this god meant to the Mycenaean communities who worshipped him" (in Daniel Ogden's 2007 Companion to Greek Religion, p. 328).