Should DUAL flight be logged as SINGLE PILOT TIME?
1) If you are under training in a single pilot aircraft (e.g. C172), it is logged as dual in single pilot. If you are under training in a multi pilot aircraft (e.g. A320), it is logged as dual in multi pilot.

2) Correct.

3) If dual (under training), the PIC name should always be the name of your instructor. The only time you use SELF is if you were PIC, and therefore the flight cannot be dual.

See EASA Part FCL; FCL.050: https://www.easa.europa.eu/sites/default/files/dfu/Part-FCL.pdf