Suggested answer:
(1) Melted is the more commononly used form in the corpus.
(2) Examples of melted and molten used in similar contexts:
All that luck-junk, peace-signs of melted lead, love beads...
His fingers feather, the matrices rattle on high, the molten lead comfortably steams at his side.
(3) In some cases, as in the example just cited, the two words are interchangeable. However, the collocations suggest that melted is a more general word, collocating with a variety of different nouns, while molten prefers collocates that refer to a particular substance or element, e.g. brass, gold, granite.
(4) Yes, one of the occurrences shows molten as a participle:
...the children watched with joy as the metal sank suddenly molten...
Read about collocations here
Terminology: adjective, collocation, participle