1 is clearly correct. And it was NOT 10km eggs, it's the fact that if you had something like less than 50 great balls, you will get much fewer great balls in future pokestops until the amount goes over a specific amount. Same happens with Razz berries or Pinaps, which you will get less when you have less.

What you were meaning is if you have several 10km eggs in your 9 eggs you will get more. This is somewhat true, but even more true is if you got a 10km egg you will get a whole streak of them, like 5 or 6 then they will stop appearing altogether until you get another 10km egg.

The second is fake. Gym activity has NOTHING to do with Ex Raids, or Raids in general.

Raids are spawned at random intervals and it doesn't matter how much gym activity there could be; Hence the chance where you can go to a legendary raid and see 0 people if you are in the wrong places at the wrong time, like say, london in winter where nobody raids.

EX Raids are spawned every week and again have nothing to do with gym turnover, but instead they are based on which gym had the most amount of raid activity, and they always happen in parks or sponsored gyms. From what i thought the park or sponsored gym in every level 12 s2 cell with the most activity will create an ex raid. I don't know but i think it is.