Question 1:
Do not enable Windows' own SNMP Trap service. That service is designed to allow Windows itself to capture other device traps, but you want the NetXMS Agent service to capture those.
You do not need to configure SNMP Traps (inside the SNMP service), unless you want your Windows 10 Pro PC to send its own Traps somewhere. In short: You do not need this to collect traps from network devices.
Question 2:
Move the Windows 10 Pro PC into the SITE1 Zone (right-click on node, Change Zone)
Right-click the zone, select properties, select Communications, select the Windows 10 Pro PC as default proxy
Add the SNMP devices manually and ensure they are in the SITE1 Zone. (Alternatively: configure Active Discovery for the Zone and wait for devices to be discovered. However, for now it is probably easiest to just add the handful of devices manually),
If you are looking to poll SNMP data (e.g. bandwidth/cpu/memory usage, etc.) on the printers/switches/router now, you should be ready to go.
Notes:
If you are looking at collecting SNMP Traps (which is something very different to polling SNMP data - Traps are packets sent from the device in question when a certain event is triggered, these are NOT used for Data Collection Items), you need to also configure each of these devices so send SNMP Traps to your Windows 10 Pro PC (might as well configure Syslog while you're at it) and add "EnableSNMPTrapProxy=yes" to your proxy agent configuration on Windows 10 Pro PC.
Your proxy agent does not require any additional configuration to act as Syslog Proxy.