Regarding sending ships on raids I'm not sure how many you can send at once, I think it's related to the level of the Destiny Carrier you have.

Stargate raids and starship raids are independent of each other, so sending an attack to a planet through the Stargate will leave the Destiny open to use, and allow you to send starships.

Hope that helps

Maximum I have tried is 4 simulatenous destiny raid, I have not ran into any limit in raid numbers.

Thanks