Am I correct in assuming taur+gwend would be Taurwen?
What would "Secret Forest" be? Thurin+taur, Thurin+glad, or Thurin+eryn?
Tawar means wood (the material) right? Tawar+tân would equal "carver"?
I beleive Taurwen would be correct. Thurinnor would be Thurin+taur. Soft mutation, then S50 au > o, then S53 > nd to nn. Which might get confused with secret land as dôr [nd-] can create that -nor/-nnor inflection.
I would have to look into eryn.
Tawardan would be forest builder I believe.
Hm. What refers to wood, the material?
I'm going to add another word for you, hidden bow cû+thurin.
Unless you're really eager to speculate about how Nandorin cogn would work.
Taur + gwend would produce Torwen.
Thurinnor seems to be a correct form for an ancient compound of thurin + taur, though it does indeed become very obscure; perhaps Thurindor would be slightly better.
Thurin + glad > Thurillad, or a later Thurinlad. These, of course, also look like "secret plain" (< lad).
With eryn I'd be more conservative; based on the examples of Eryn Vorn and Eryn Galen, I'd suggest Eryn Thurin here.
Tawar is an alternative form of taur, meaning "forest". The sense "wood (material)" comes from Noldorin (=draft-Sindarin). Whether this sense is still applicable in late Sindarin is a good question; given taw, I'd say not.
For "carver", i.e. "carpenter", we actually have an attested Quenya word: tautamo; a direct cognate of that (i.e. derived from taw + tân) would be Tódan.
Cû + thurin can just as likely yield Cúthurin, following the exact same pattern as Cúthalion.