Self-reporting is not a thing in the US, so yes you have to send all SAT scores directly. In most cases the scores have to arrive by the application deadline.
As you are in an English language secondary school many universities will not require the IELTS, and for those schools there is no worry about when your scores arrive. Check for each college to be sure what their rules are.
I am assuming that you have / expect to have top choices in the UK (or elsewhere), which is why you are only applying to universities for which your odds of admission are teeny-tiny. Even if it is only ‘worth’ your applying to super brand names (b/c of your UK/other options) I would prune your list further. For a start, CalTech and Dartmouth are mutually incompatible environments (not to mention that CalTech took a total of 19 international students last year). NYU is an outlier in the group- why is it there and not (say) MIT?