Getting into an US University as a British student

I completely understand what you mean, I think my average grades at GCSE were also due to me not really knowing what I wanted to do after high school and therefore not being very motivated, but the past year my motivations have completely changed and I have become super driven and enjoy learning much more. I also fell in love with some very good schools like WashU (unfortunately for me as its extremely unlikely I would get in). I am considering other schools ranked around 30 but of course I would prefer WashU!

I think the point here is if you want to come to the USA you will want to be looking a tier or 2 down. That could well result in getting offers from US universities that would just not be worth the cost compared to the sort of unis you might get into in the UK. Go look through the sub forums for your target schools, understand the international acceptance rate and that internationals will be held to a higher standard when from the UK, not lower. Google common data sets. Again, what schools would you expect to get into in the UK? Not top tier.

Are application deadlines for US uni’s similar to UK deadlines?

No, they go from November 1st for Early decision/Early Action, to December 1st (for the best scholarships) to January 1st (for the most selective colleges) to March 1st (for the less selective colleges) with many having dates on jan 15, Feb 1, and Feb 15.