Get some of these[0] and it should be no problem.

[0] EarBuddyz 2.0 Ear Hooks and Covers Accessories Compatible with Apple AirPods 1 & AirPods 2 or EarPods Headphones/ Earphones/ Earbuds (3 Pairs) (Clear) https://www.amazon.com/dp/B019BREFE4/ref=cm_sw_r_cp_api_i_EJ...

Yes, although it may depend on the shape of your ears. I trained for the NYC marathon and often (but not always) wore AirPods. I never had them fall out.