Noldorin is the conceptual precursor of Sindarin, "draft-Sindarin" if you will. It largely belongs to the 1930s-1950s, whereas mature Sindarin is later. You are right to be cautious - many Noldorin words cannot be used in Sindarin without some adaptation, due to Tolkien's conceptual changes. For example, Noldorin auth ought to be oeth in Sindarin; the difference arises due to slightly different historical phonological developments.
Feel free to ask when in doubt about a Noldorin word.
Note that whilst most Noldorin words can be adapted to Sindarin at need, the same is not true for even older conceptual stages, such as Early Noldorin (1920s, marked as ᴱN on Eldamo) and Gnomish (1910s).
Regarding bín vs. 'wín:
There are two different and mutually incompatible theories as to what the 1st person plural inclusive pronoun ("we [including you]") in Sindarin should be. Of course neither form is directly attested, so we are forced to reconstruct something.
One theory (which I believe is also the older theory) takes the attested Common Eldarin form ✶we, from which the equivalent pronoun in Quenya derives, ve. This results in the form gwe in Sindarin, and its possessive form would be gwín, lenited to 'wín.
The problem with the above derivation is that it does not fit in with the 1st person plural inclusive suffix found in a document 1969 (which is very late in Tolkien's life): -b, attested in athab. In Quenya, as well as with other pronominal suffixes in Sindarin, we always see a direct relation between the suffixes and the independent forms, but there is no straightforward way for -b to be etymologically related to gwe.
As such, an alternative theory arises. Note that -b, as mentioned, is attested in athab. This contrasts with other pronominal suffixes, where the vowel before the suffix is o (e.g. athon & athof, attested besides athab). Given this, the only reasonable etymology for this -b is from ✶-kw(e). The likely explanation is that the older ✶we is further reinforced by attaching ✶ki (2nd person singular [informal]) to it, emphasising that the listener is included. With this in mind, and since other pronominal suffixes are consistent with their separate forms, it is reasonable to suggest that the separate pronoun would be ✶kwe > pe, and thus its possessive form would be pín, lenited to bín.
Both theories have their advantages and disadvantages. The gwe theory derives the pronoun from an attested CE form and goes for analogy with Quenya, but raises the question of why the Sindarin pronominal suffix -b would have a different etymology. On the other hand the pe theory relies on a reconstructed etymology based on that suffix, resulting in internal consistency in Sindarin, but at the same time it claims that the CE ✶we, which survives in Quenya, is altered in Sindarin's history.
I personally prefer going with the form that is based on something attested in Sindarin itself (i.e. pe). It would also be unsurprising to find differences in the Sindarin and Quenya pronouns, since we already have some other differences attested independently. But I'll leave it to you to judge which form you find better, given the above discussion.
