One-to-one is used when you talk about transfer or communications. You may use one-to-one when you can identify a source and a destination. For eg., a one-to-one email is one sent from a single person to another, i.e., no ccs or bccs. In maths, a one-to-one mapping maps one element of a set to a unique element in a target set. One-on-one is the correct adjective in your example. See Free ...
Some people say a dog=one, dogs=ones, the dog=the one=that, and the dogs=the ones=those. It's a rule of thumb, but what I found was that this is not always correct.
The first one is the indefinite pronoun referring to country —that is, one country, a country. The second is the indefinite pronoun denoting an indefinite agent—it might be replaced with somebody or anybody or (usually in colloquial registers) you. Still in still life has the sense not moving. Still lifes (not still lives!) are works of visual art which depict inanimate objects such as ...
However, "one and only one" adds emphasis to the fact that there is only one, and draws attention to it. For example, the student who is the only one who failed, might feel more ashamed if the teacher uses "one and only one", as the teacher might be perceived as purposely drawing attention to that fact, for whatever reason.