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There are many contributing factors to high ping, if you have a poor WiFi connect right now then this will likely improve your overall ping as you connection quality improves. If you have a good WiFi connection, though this router is particularly snappy for throughput you are unlikely to be gaining any substantial ping delay with your existing equipment. The largest factor of high ping sits outside your network.
It won't slow your ping down. Ping is going to be impacted by your ISP far more than anything else, though. So if your ping is bad, look at your ISP first and your router second.
That depends on if your router is slower than your internet. Meaning... if you only hooked up a device to your internet is it operating slower with the router? If you can't notice, its not your router.