The "oil service" and "inspection" lights are determined by algorithms, in the case of the oil service it would hinge upon number of cold starts, amount of stop-and-go driving, duration at highway speeds, stuff like that, so you can get optimal use of the oil. I think the same indicator lights have been in use in BMWs at least since the E30 models, consequently you should have a series of green lights that extinguish as the oil change interval draws near, then yellow lights I believ, then red or orange when the interval has been exceeded. To get back to the full display of 5 green lights you need to use the reset tool, or have it done for you. Since this car is relatively new to you, the indicator lights were probably unfamiliar, but I should think that something should have been illuminated on the dash (yellow lights perhaps). See the owner's manual (if still available) to read up on this.
I'm not aware of oil viscosity being measured differently in North America vs. Europe, although I could be wrong. I'm not convinced that synthetic oils are worth the price differential, or even make any difference, in older engines. For sure some cars come direct from the factory with synthetic oil in them, but these are brand new cars, with modern engines made to closer tolerances and with better materials than before, and therefore can make better use of the qualities of synthetics. That's my read on the situation, your research and preferences may indicate otherwise.