Re: Leaking bathroom faucet under sink
That last pic is the actuator rod for the drain stopper, there is no seal here, it's a direct open hole and any water splashed on the top side of the faucet/actuator rod, will certainly find its way down through that hole. This hole is only through the decorative housing of the faucet, it does not pass through any water passages or through the inner workings of the valve itself. So, other than top side splash, this would not be the source of your leak.
Your actual "valves" are separate from the spout, check your hose connections from both your hot and cold lines where they connect to the spout. Also, give the spout and handles a good wiggle to see if they are loose on the surface of the sink, if they are, then it could still be a surface leak rather than a supply leak.
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