As a self-learner, what to do with books providing exercises but not solutions?
An inability to confidently answer the questions in a text book in general is an indication of not having mastered the material.* If you are not 100% confident that you are solving the problems correctly, go back and read the material again. You will not be able to use the skills in research unless you know the material without an answer key.

*For a graduate class I used to teach there was a problem in the textbook that I could not solve. No matter how I thought about the problem, some information was always missing. I am friends with the author so emailed him for a solution set. I was too embarrassed to admit I couldn't solve the problem and figured the answer key would be helpful anyways. The answer for the problem in question was "Not possible with supplied information."