Diagnose Faucet Issues

What happens here

Begin by observing the faucet's issues. The handle is leaking when operated, with water coming out around the stem. Additionally, the water flow from the aerator is not a steady stream, indicating a potential clog or issue with the aerator itself. Pushing the pop-up drain plunger (the small knob on the faucet base) also appears to affect the water flow from the aerator negatively.

Goal: Identify and confirm the problems with the Delta bathroom faucet.