Questions about svm classification

I am learning the basic concepts of classification learning. And i got two questions as follows:

  1. Can the training set and test set be two independent data sets? For example, can I use the weather characteristics of two conditions(i.e. sunny day or not) in city A as a training set and test on the same characteristics in city B?

  2. If independent test data sets can be used, can classifiers be used to test data with only one category? Take the weather as an example, train the data of city A to test the data of city B that only has sunny days (one category). Is this classification operation reasonable?

Thank you very much for your attention!