With these exact words, yes it is. But you could say "É demasiado cedo" (but never "é demais cedo" or "é cedo demasiado").
This in European Portuguese. Don't know if Brazilians use this alternate wording.
Yes, this applies for Brazilian Portuguese too. You can also use "demasiadamente", in the same place as "demasiado" (the latter is an adjective working as an adverb, the former is the actual adverb, and they both mean the same thing).
Almost all romance languages put adverbs after verbs and adjectives after nouns. If a modifier comes before a verb or usually a noun, it is considered a poetic tone. "Um velho cachorro" has a different meaning than "Um cachorro velho".