you can check all of your questions by reading the configuration guide for the RV260P here:
about your questions:
inter Vlan routing means allowing routing between different Vlans in your case the private Vlan and the DMZ Vlan for example.
The firewall feature can provide access rules between the different Vlans as required.
The device supports POE verify how much power is required by your access point to be sure the router can provide the necessary power.
pag 57 of the above guide explains how to configure per Port POE, default settings is 15 W, max 30 W.
Regarding your list I would say:
1-3 yes supported by firewall feature see pag.77 and following
5 see the static DHCP feature on page 60 it is what you want.
6 DDNS yes see pag 52 of the guide
7-11 yes with firewall feature with appropriate access rules configured see firewall section page 77
Hope to help
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