Gateway to work with mesh bulbs and xiaomi sensora

Hello, I have the Xiaomi gateway 1 and several sensors. Now i have yeelight mesh downlights but they don’t work with thia gateway.
If I buy the xiaomi gateway 3 will the previous sensors work with this gateway3? Will the mesh downlights also work with this gateway3?
Or the mesh downlights only work with the yeelight gateway? In this case will the sensors wirk with the yeelight gateway? Or i need to have both gateways? Will both gateways, sensors and mesh bulbs be integrated in Mi Home App?
Can I link them to smart thinks app like the yeelight app?
Thank you.
PS - i am in europe.