Do I have to come back to the US for a certian amount of time before I can re-enter?
From Chapter 2, Annex A of the manual:
"...There is no restriction on the number of visits a person may make to the United Kingdom nor any requirement that a specified time must elapse between successive visits. The fact that a person has made a series of visits with only brief intervals between them would not, in the absence of any other relevant factors, constitute sufficient ground for refusal..."
And from Chapter 3, Annex A:
"...There is no objection to a person, who was given leave to enter as a visitor, undertaking a short course of studies which will be completed within the period of his visit...."
Hope that helps!
As to the part-time classes: The key words in the above paragraph are "relevant factors". It's axiomatic that when you tell the IO that you will be attending part-time courses, they will move to the second level of enquiry. I suggest that you bring the descriptions of them and your registration (tuition receipts, whatever) so that the IO can review them. The first entry is relatively easy, it's the 2nd or 3rd that you need to plan for...