Being an American in the UK for over 7 years now and having done my PhD here in the process I can understand how being completely outside the system is so confusing. I was in England for the first 7 years and am now in Scotland and they don't have GCSE or A levels but things called 'Highers' which are slightly different?!
But first to your questions (and others can correct me if I am wrong):
Qualifications - that is pretty much anything that ends in a certificate or diploma. An A level or AS or GCSE (in some subject) is a 'qualification' as is a BA, MSc, or PhD.
Credit - I am assuming that this information is regarding transfer US college credit. If they did an A level in Maths then they would receive 8 college course credits. (I could be wrong here)
Subsidiary - Like a minor. In the early days that would shave been like doing about half the work.
I just had a discussion with my English colleague in my office and she had a right rant in filling in some blanks as when she did GCSE they were changing from what were then called O levels.
Regarding the grading of the GSCE. It is generally graded from A-G. In Maths there is the Basic course that is graded only up to B and the Higher course that goes to A. My colleague assures me that one of the big changes from O level to GCSE in Maths was the removal of Calculus. She only did advanced algebra and trigonometry.
Also, the GSCE is the most basic qualification, so like a HS diploma, but you get it at about age 16. The A levels take up the following two years.
According to the wise woman behind me - the A and AS level thing has changed and apparently now most kids take 5 AS levels in their first post-16 year and then drop two and do 3 for A levels. After that they go to University.
Here is a bit of information that may be useful:
http://www.britishcouncil.org/usa-education-uk-system-k-12-education.htmThe H1 and H2 vs A and AS is a difference in how the two testing authorities do the ratings - so AS=H1 and A=H2. Since the AS is 'picked up' along the way to qualifying for the A level the WES would award only 8 credits for the A level.
I hope this makes sense and isn't completely off base!