Which countries accept the written UK exams?
Only the UK (and all the flight schools that operate outside the UK but under the auspicies of the UK CAA, which are basically the three schools in Florida, one in SoCal, one in Canada). The UK written exams are specifically NOT accepted in any other JAA state - they only start recognising things mutually once you have the full PPL and up.
Is there some sort of interview with embassy to do your PPL in the US?
Yes, you need to be "interviewed" at a US embassy to get the M-1 visa, which you need for training in the US. Details in the link above. Also you need TSA clearance. In your case, you might be able to get this done in Baghdad.
what does she mean?
What she means is that if you go to SA to do your full flight training there, you'll be issued a SA PPL, which is NOT JAA (JAR-FCL) compliant. Thus, in principle, this PPL only allows you to fly SA-registered planes (around the world, that is). The UK CAA is an exception and makes it rather easy by recognising foreign ICAO-compliant PPLs (which a SA PPL is) for flight on a G-reg within UK airspace, subject to a few limitations, but not all European CAAs do the same. So to fly a G-reg worldwide, or any JAA-reg worldwide, you'll always run into the trouble of getting your SA license validated. Plus the correspondence every now and then with SA instead of Gatwick, plus getting and maintaining a SA medical, plus the hassle that SA doesn't do class ratings for Single Engine Piston, but requires type ratings for each different (sub)type, makes this inconvenient. That's why you will want a UK-issued JAA (JAR-FCL) compliant PPL eventually. And a conversion from a SA PPL to CAA PPL comes down on doing all ground exams and the flight test anyway if you don't have a lot of hours so is not worth it.
So her suggestion is to only do the actual flying in SA, but do the ground exams, the R/T practical and the flight test in the UK. Very possible but you'd have to find a place in the UK on your own that's willing to go along with something like this - they're not going to make a lot of money off you.
My advice: if you decide to go abroad for your flight training, pick a CAA-approved school somewhere (3 in FL, one in SoCal, one in Canada) since they can do the whole package (ground exams, flight training, R/T practical, flight test) in one place.
But it is true that all your flight experience as P/UT and (solo) PIC of a SEP(A) counts towards license issue, not just the flight experience you have had in the country that eventually issues you your license. So doing a few hours in one place (SA) and then finishing off in a different place (US, Scotland) is very possible. Do make sure you keep an adequate training record though.