You can transfer if you already started your first year at uni. The requirements vary by university though - some unis require that you finish 60 semester/90 quarter units (the equivalent of two years study) before applying to transfer and others allow you to transfer before that. Check the university's undergraduate page before you do anything.
As far as the SAT or ACT, you won't need to take it. That's only for those applying for their first year of university. They may ask for the scores if you did take it though. They might also ask to see your high school grades, especially if you haven't completed two years of study yet.
As for the transferability of the credits you've already earned at your home university, you should contact the undergraduate admissions office at the US university and speak to an advisor. That person will determine what courses will transfer and which won't and again, it will be different for each university.
If you are currently studying at a university in the UK, it is very possible that if you transfer, your first year in the US will be very close to what a freshman year looks like. You said you studied high school in the US so I am assuming you are familiar with what the General Education requirements are in the US university. Those classes you need to take and complete within your first two years concurrently with the classes for your major. Having said that it doesn't mean it will push you back a year. If any of your courses transfer, you might be done a semester or quarter early or have fewer classes to take in your final semester.
(Once you have spoken to the admissions officer about which of your courses will transfer, you can check the degree requirements for your major on the uni's website to see how long it will take you to finish your degree and if you will finish on time).
Good luck