Yes, that will absolutely cause issues. Even a small cut in the outer sheath can cause issues, the connector needs cut off and re-crimped. Takes about 2 minutes with the proper tools, which can all be bought at Lowes or HD or get a tech out to fix it.

It’s best sometimes to just reset them through the controller and leave them behind. Buy new at the new place.

If the router has 1 gbps ethernet port, the max it will provide is about 940mbps. It’s the PHY limit of a 1gbps NIC.