It looks like the exact same model faucet I installed in my kitchen years ago. It is, in fact, an utter piece of garbage, and anything you try to do to fix it will be, at best, temporary.

The problem is in its basic design: the retractable hose WILL leak eventually, and all the leaked water will drip down into the base, which WILL mineralize and/or corrode.

I finally got sick of it and stopped wasting good effort on a bad faucet. I replaced it with a tall-neck design, where the retractable hose pulls down from the neck, rather than up as with the old one. Less than an hour of work, and now no more aggravation!