Masters/PhD study in the US

Yes, there are terminal masters degrees in the US. These are usually MS but occasionally there are MEng programs too. If you think you might want to do a PhD in the US then that is the route you should go, there is a lot more funding for PhD students compared to MS students and you can just drop out with an MS once you've completed the requirements.

2. Just the GRE

3. Company manager should be fine but they usually expect academics or say people in the industry you worked in or that the PhD is in. I got my tutor, my thesis supervisor, and a CEO/academic at an American university that had supervised another project I had worked on, before I decided not to apply.

Regarding going to the US for MS study, be prepared to pay for it, financial support for masters students is pitiful compared to bachelors or PhD even at top universities. This also applies to applying for degrees too, the GRE is an expensive test and you might end up with application fees on top of that. Also be prepared to repeat content that you've already studied during your bachelors, American bachelors degrees in engineering teach to a lot lower level than they're made out to be and a lot of the content is pretty much catching up to your education.

For PhD study it is really long and much more gruelling than in the UK or Europe. You're catching up on taught content, for which you're expected to get good grades to continue your PhD, you have to teach or work as a research assistant for a fairly high proportion of time that you're there, and you have to do your actual PhD. While the length of a US PhD is supposed to be 5 years, 6 is more typical and it's fairly common to go much higher than this, 10+ is not impossible. Despite the stipends in the US looking a lot higher than in the UK, your cost of living is also much much higher and this will typically outweigh the salary difference. Even at pretty high ranked universities it's common to get less than $30k per year which is an absolute joke when you have to pay for health insurance, running a car, flights back home, the expensive rent that comes with living vaguely nearby a university.

If you're not scared off by that then add Embry-Riddle to your list, they're also a very respected university for aero.

As for other countries to try, Canada, Australia, the Netherlands, Singapore, and Hong Kong are all very good places to do a PhD with very good funding available for internationals and accessible to English speakers.

Thanks for this! Its been really helpful, so I think I'll apply for the PhD programs at those unis rather than the masters. I guess my only problem is that do colleges accept BEng students for PhDs. For example, when I look at the Stanford website for their PhD program they say that you must have done a masters before applying, so isn't that not limiting me to do the masters course first instead of going straight for the Phd ( https://aa.stanford.edu/academics/graduate-programs/doctoral-program). Also, I'm a bit worried since I don't know who to get for a reference, I mean so far, I have done an internship so thinking I could have my manager, and then I can have my academic tutor, but I don't know who to get for my 3rd referee.
If I may ask, are you currently enrolled in a graduate program outside of the UK?
Thanks