Solved

Rain problem

What probably happened was that it was still raining during qualifying and, as your screenshot shows, it wasn't anymore at race start. Now basically the game goes for two things, the hierarchy of setups which is main strategy > advanced strategy and a check if the tyre group the tyre belongs to (dry, rain) equals the given weather at race start. So you did setup a dry tyre in main strategy and since it was raining the check for qualifying if it's the appropriate tyre returned a false, so the game proceeded to the advanced setup and applied your choice of Wet tyres in the rain starts option for the qualifying. 
Afterwards the rain stopped however and thus your main strategy tyre brought up a true on the tyre check for the race and thus the game just proceeded with your main strategy for the race start. 

The track conditions play no role here, only the actual weather. Which is somewhat of a problem lately after the change that made drying up taking almost an eternity. If you'd set up Inters in main strategy then the check would be true for the qualifying and thus that one used and false for the race and the game would've went on to the advanced strategy looking for a dry tyre to choose in the rain stopped option.

What I'm not entirely sure of is if the two advanced options have a hierarchy amongst each other in certain situations or if only the appropriate one is selected exclusively. There were situations pointing to hierarchy, as in a dry tyre in the selection for if rain starts might be selected if both main and rain stops both sport rain tyres for some reason and it's dry weather. But maybe that was the tyre bug (or problem preventing the game to successful save the strategy) that sometimes put you on tyres, mostly mediums, you choose nowhere anywhere in strategy, just coincide with a selected tyre.