You have misunderstood the warhammer. The hammer IS the spike; they used the term differently back then. On a warhammer the "hammer" was the sharp spikey part, not the flat bludgeoning part. The flat bludgeoning part was called a "poll" (which literally means "head"). Another term for warhammer was "pollhammer". A "pollaxe" was an axe with a poll on the back. Many confuse pollaxes with halberds.
The lance wasn't replaced with pistol and sword. Heavy cavalry units such as the Hussars continued to use lances into the 18th century.
"Arming sword" and "side sword" referred to the same weapon - i.e. whatever sword was carried on the hip. Typology didn't matter.
Plate armour reached its full potential and technological advancement in the 16th century, not the 14th century. The 14th century is when it first started to appear.
The best armour was always obscenely expensive. The Elizabethan period was no exception. In the Middle ages it required the combined wealth of several villages to field one single armoured knight.