Yes but…
No. And the question makes me think I may need to clarify what “yes” actually means to your first question.
Wireguard makes its own network and assigns IP addresses on it to clients as they connect. If you put 192.168.1.50 in server then that is setting the address of the gateway on that network. So when your mobile phone connects it gets assigned the IP 192.168.1.51 on that network and is told the gateway is 192.168.1.50. Wireguard will listen on 192.168.1.50 and answer any queries it can and forward the ones it can’t on to the rest of your network.
Note that Wireguard is not accessible at 192.168.1.50 on your normal LAN. Nor is your phone accessible at 192.168.1.51 on your LAN when it’s connected. In fact there may be another device with that IP address on your LAN since you said you use 192.168.1.0/24. Your router has no idea Wireguard has made this subnetwork so it could give that address out via DHCP. That is quite confusing possibly problematic, my advice would be don’t do that. Pick a different subnet for Wireguard, 192.168.2.0/24 seems fine.
Also have you tried removing client_allowed_ips and seeing if that works? Nothing else is jumping out at me but I don’t use that config myself, I want all traffic to go through my VPN when I connect personally. I would suggest at least trying without it and then if that works you know that’s the issue.