Look at the test list on this website for an extended list of a variety of tests of critical thinking.
2. Is critical thinking best taught in a separate course or infused within existing courses?
The question assumes that it will not be both. Actually, it would be best to do both if conditions permit. See Incorporating Critical Thinking in a Curriculum.
3. What is the best way for adults to improve their critical thinking skills?
Focus on being Reflective, seeking Reasons and seek and compare Alternatives. (This is "RRA".) See information on self teaching.
4. Do you know of any good critical thinking tests for children under 8 years old?
No, in part because because it is difficut to communicate sophisticated ideas or questions in writing. For example, it is difficult to ask them in writing what is assumed in a particular line of reasonsing, yet we know that they can do this when they figure out what a teacher is thinking or committed to, perhaps when a teacher gives a reason for giving another student permission to do something. Interview tests are probably required for assessing the thinking of young children.
My associates and I developed very labor-intensive assessment procedures for assessing deduction ability in young children (ages 6-8). See
Ennis, R. H., Finkelstein, M., Smith, E., and Wilson, N. (1969). Conditional logic and Children (Cornell Critical Thinking Readiness Project, Phase IIC). Ithaca, NY: The New York State College of Agriculture at Cornell University. ERIC # ED 040437. Available from ERIC; results are summarized in Ennis, R.H. (1971). Conditional logic and primary school children: A developmental study. Interchange, 2, 126-132.