Gateway keeps flooding the network with arp requests

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By itself, 100 arp requests every 5 seconds can not cause any network lag. What causes the router do that, and what happens if it gets a response, is a much more important question.

Is it possible for the gate to be poisoned in this way?

The sad answer is yes, home gateways can get infected by malware, with vulnerabilities ranging from vendor's backdoors through default WiFi passphrases deductible from MAC address which is broadcasted in the beacon frames combined with easy administrator passwords used "because the WPA2 is unbreakable so who cares about admin password" down to management ports open at WAN interface. Also an infected PC in the home LAN can silently keep trying to log as administrator to the gateway router using vocabularies of popular passwords.

So if re-flashing the router firmware, using TFTP during boot if supported in order to minimize chances for survival of the malware, helps, there is a high probability that your box got exploited.