Take a look at your Traffic Statistics page to see if you are getting dropped packets or errors. This would help indicate a networking issue.
To get there, log in the router, select
Status on the top menu then
Statistics on the side menu.
LAN Statistics
Sent : 8002496
TX Packets Dropped : 10
Collisions : 0
Received : 5921546
RX Packets Dropped : 0
Errors : 0
You don't need to worry about Cat6 cabling unless you are having a connection problem or lots of dropped packets. My network is entirely Cat5e running at Gigabit speeds with no issues. Cat6 is guaranteed to support the bandwidth requirements of Gigabit ethernet while 5e is not guaranteed but very likely to handle it.
Other than this, I would have to defer to Lycan's expertise to help further.
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