Welcome to Just Answer,
If this is a single lever faucet then you will probably need to replace the cartridge in the faucet to correct this problem
OK. That doesn't sound too complicated. However, the first obstacle that I have to overcome is how to get the handle off in the first place. Below you will see some photos I took a few minutes ago. When the handle is in the extreme upright/on position and the hot/cold label plug is removed, I do see what looks like a weird kind of "inside nut" (???). You can see in pretty clearly in the closeup photo. Should I try to buy some sort of tool to remove or loosen this? If so, what kind of tool should I ask for?
Sorry, I guess I don't have a handle on how to send you the photos yet. Give me a few minutes to figure it out.
You should see a tree icon in the tool bar of your chat window. Click on the tree and a dialogue box should come up
Yes, I saw that. However, the photos evidently have to be posted on some sort of photo sharing website. I'm working on that now.
The pics should post in the chat window. We has experienced file upload bugs recently so it may not work.
Try this and tell me if you can see them.
Can you see the pictures?
Yes. You need to loosen the allen set screw then pull the handle off.
Ok, I'll try that
I don't mean to argue with your analysis, but no size of allen wrench will engage the nut. It looks to me like there is a round center post INSIDE the nut. Isn't there a particular tool for this kind of nut? If so, what's it called?
The allen screw is probably stripped. If it is then your only option is to either go to a hardware store and see what they have for a screw extractor or you could try to drill out the set screw. But drilling it out is not an option I would recommend. Allen screws are often hardened and if you slip while drilling it out the handle is junk.
Do you have any more questions?
Sorry to step in Rick.
In the picture What I see is an ANTI-THEFT ALLEN SCREW you can ask if they have this at your hardware store or I know you can order one at Mc Mastercar or Grainger on line.