The extent of Sony's interest in PS+ subs and GTS is something only a Sony executive knows for sure, but I also think it's myopic from your part to not see that everything is connected. I'd doubt that PD, being a subsidiary of Sony, is not integrated in their broad strategy. Ironically, Gran Turismo is a game that supports 4K and HDR (I know these two are becoming common, but for sure this is a requirement forced by Sony and not only a design choice), PS VR, and iirc, even supported 3D once just to add value to Sony in their TV business. Wasn't it even used to showcase 8K TVs recently? GTS is integrated into Sony's strategy to value its games business AT LEAST.
Would be shocking to me if Sony neglected all the synergies between its products at least inside the same division. Most probably they're much smarter than you think and see GTS and a good seller of PS+ subs, among other things.
Yes, indeed. But offline is obviously not the focus for them. They barely created any offline content using the new tracks and cars.
As for not becoming a paid service, isn't it the goal for pretty much everyone right now? Why would they stick to the old model of making one sale when the world is showing there's a lot more money do be made when you engage your audience for longer, with live services?