What if I bring hospitality AP "out-of-the-box" and connect it to vlan 20 with an assigned DHCP, does it take the DHCP immediately. or I need to configure the AP port to VLAN 20?
You do not need to configure the AP port in this instance.
I am a little bit confused because as I've read Aruba IAP only work if they are connected to native vlan. Should Hospitality APs be connected to Native VLAN or they can be connected to any VLAN "not native"?
You will be connecting the AP to a port. If the port is configured as an access port the AP will attempt to acquire an IP address from the VLAN configured on the access port.
If the port is configured as a trunk, the AP will attempt to acquire an IP address from the native VLAN configured on the port.