Prepositions Meaning – Difference Between ‘Do Good To’, ‘Do Good For’, and ‘Do Good By’

To think much of someone is to think highly of them. To give them high regard or respect.

It is very often seen in the negative. I don't think much of him is used to refer to someone you dislike or disrespect for some reason.

I've never come across the expression being used in either of the senses that you quote in your question.

So your example; We don't think much of people who readily believe rumours indicates that such people are not highly regarded.

'Yes' can be considered the baseline - I can't think of any context in which using it would be inappropriate. (It might come across as slightly over-formal on some occasions, but more likely no-one would pay attention to it) Any official/formal speech will most likely use 'yes', as will almost all written usage.

'Yeah' is an informal equivalent to 'yes'. In casual conversation you are more likely to hear 'yeah' than 'yes' unless the speakers are making a deliberate effort to be precise with their speech (the reason that 'yes' can potentially sound overly-formal). On the other hand, a written 'yeah' will generally only be used when writing dialogue.

'Yah' would be 'yeah' spoken in a different accent. I would personally associate it either with a non-native speaker (the German accent in particular), or with native speakers who are uneducated/unsophisticated.