Fòram na Gàidhlig

I have some questions about the conditional tense (technically a mood, not a tense, I know...) of 'to be' in Gàidhlig.

In the Taic lessons, it's taught as follows:

1. Bhithinn / Bhiodh / Bhiomaid - for positive statements

2. Cha bhithinn / Cha bhiodh / Cha bhiomaid - for negative statements

3. Am bithinn? / Am biodh? / Am biomaid? - for asking a question (interrogative)

4. Nach bithinn? / Nach biodh? / Nach biomaid?

As you can see, 3 different forms are taught for each of the 4 categories above. It explains that there are separate forms for the 1st person singular - Bhithinn, and 1st person plural Bhiomaid (or Bhitheamaid for emphasis), and that Bhiomaid is becoming less common, and particularly in spoken Gàidhlig is being replaced by the regular Bhiodh.

I wanted to clarify if it's definitely ok to replace Bhiomaid with Bhiodh in the spoken language, because I'm looking to sound as natural as possible, and which form is used in writing (both formal and informal writing, that is)? Is Bhiomaid used in writing formal letters and in books etc?

Thanks.

"Bhiodh sinn" is acceptable in all situations and not generally considered informal.

Thanks. I have another question - I noticed in the book 'Scottish Gaelic in 3 Months' that it teaches 'bhithinn' as 'bhinn'. Is this a misprint, or just another way of saying 'bhithinn'?

Also, another grammar book I was looking at says that 'bhithinn' = 'bhiodh mi' - was that just an example saying 'bhithinn' is equivalent to 'bhiodh mi', or is 'bhiodg mi' actually used?

No, "bhiodh mi" is never used.

I have never seen the "bhinn" spelling before, but it's entirely possible that people shorten it like that when speaking. I have never paid attention to that though.

There's a chapter in Blas on short and long forms, I forget which page.

In particular irregular verbs have long (stressed) and short (unstressed) forms. The variations go from hiatus with emphatic endding > hiatus > long vowel > short vowel > reduced vowel > no vowel, though not all verbs have all "stages".
So bhithinn/bhitheamaid are the 2nd most stressed forms, bhiomaid/bhinn are the next step down with /iə/ and /i:/ respectively. Written the same way but one down are /vimɪdʲ/ and /viNʲ/. It's just one of those GOC weirdnesses that they recommend (as far as I recall) the reduced spelling bhiomaid but not bhinn.
Some don't show any spelling variants at all but vary in pronunciation, in tha the vowel goes from long to zero depending on the stress pattern.