For the most part Cat6a is find for home use. There should be no latency difference between fiber and copper. Make sure your Router has a enough CPU power and a good amount ram (4gb-8gb) as packet filter and firewalls can eat up a lot of memory and so can other such services. For the most part fiber is not needed, as Fiber is mostly use in the 10 Gigabit + (example 40Gbit and 100gbit links) or very long run over 300 meters. Also fiber is much harder to work with and test equipment can easily get into the 4 digit range.
The distance between it so small it should make no difference.It could be a configuration issue or the computers them self could be an causing the issue . Also a better way to test speed is to use a tool call iperf which is used to test speed and jitter on the line. I would get jperf as it has a gui and is much easier to use.
Firewall and ip blocking are all done on the router end and that is Layer 2 switch and does not have that function. One way is can set up multiple subnet ,for example one subnet you can use and the other your kids can use. This would allow you to filter the ip address of that subnet. Vlsm Calculator is good tool to help you break up your network in to smaller subnets. Then you have to setup multiple Vlans or have multiple switches each connected to different port on your router. There alot of tutorial online on how to do this. If you have any question or do not understand something i can help you as and walk you though it.