Are Unit Testing, System Testing and Component Testing subsets of User Acceptance (UA)?
They are not so much subsets as much as different phases. Systems testing is probably the one that relates most to User Acceptance Testing.
Unit testing is done while writing the corresponding application code and is at the level of "When I call this method internally with these params, I expect this response". This is before any other testing can be done.
"System Testing" is a bit vague. Assuming it means integrated testing this may be where User Acceptance is defined for a given organization via manual testing or it may mean automated integrated tests, for example UI feature tests that test that the code, the UI and the database all work together.
"Component Testing" can either mean the unit tests written for a component or (more likely) whether components can work together. This would be integrated testing and would be done after Unit Tests but before User Acceptance Testing which will usually be manual.