i think you cannot port forward Dlink by TM and also cannot apply Google DNS always TM DNS due Firmware by TM

buy you own router can do port forward

Tell us how much you're willing to pay for a router
No. Most of them are not

I think you may have confused some stuff

Firstly, what service is this that required these ports

2nd, a PoE switch is just a switch that also supplies PoE Power
So that say, you can connect 16 Cameras to it and then to your router, and the cameras get powered by your switch

Don't connect it to the modem

I wouldn't worry too much about the multicast address? Just forward those ports

EDIT: I found the source

https://support.hp.com/sg-en/document/ish_9047541-7890382-16

They mention disabling IGMP Snooping
I believe this is on by default on TM routers, so look into that