1. Dual no need to have a signature under JAR rules but the yanks sign anything
2. Solo so PIC
3 Dual then solo for the 2 hours PIC
4. dual unless you agree before hand with the instructor you are PIC if in doudt dual
5. Dual if he has signed the tech log as PIC. If you sign the aircraft out you are PIC.
You can't log PICUS unless you are doing a flight test and pass or are doing and intergrated cpl/ir course.
Usually in the uK know one signs log books but the yanks seem to sign everything in what ever pen comes to hand.
I would advise in the future you have a US log book and let them scribble what ever they like and then keep your proper log book away from the CFI's unless you decide to complete a FAA rating. Don't let them know you have a JAR log book because it really will hurt a FAA instructors feelings if he thinks that his comments on your life, attitude and flying ability arn't recorded in your log book for everyone to see for the the rest of your life. Although it is quite amusing when you chuck the FAA one in the bucket after your weeks flying, the bottom lip starts quivering.
Its really not a daft question and as you say UK FI's give very different opinions. And the rules are completely different under FAA rules.