I would say that the answer is 'No' to all of those.
You need to use 'between', rather than 'among' for all of these phrases:
...choose between English, French and Russian as their first foreign language.
...a choice between different suppliers at an earlier time.
...choose between two or three different options.
This is because there are a limited number of options which you have to consider individually. For example, you have to decide whether you would rather study French or Russian, Russian or English, English or French. You need to look at each of these options separately, so we use the word 'between'. The idea that you use 'between' for two things and 'among' for three or more is simplistic and very misleading. For example, one of the commonest errors here on italki is a question such as this 'What is the difference among 'say', 'speak' and 'tell'?', rather than 'What is the difference BETWEEN 'say', 'speak' and 'tell'?'. You should not automatically think that you should use 'among' simply because there are three items.
By contrast, it is correct to say ' elect a temporary president from among its members'. This is because there are a large number of unidentified members. In this case, we are thinking of the members as a 'pool' of unidentified people, hence the use of 'among'. 'Among' is less precise than in 'between', and often means 'in the midst of (a group or crowd)'. 'Between' would be possible, but unlikely, in this situation. If you said 'between' in this context, we would expect there to be maybe three, four or five named candidates.
I hope that helps.