If have power of attorney over my mother, can she sell any of her stuff without me approving it?

Just one more thing, you don't have POA "over" your Mom. She has assigned you as her representative only when she is no longer competent to make her own decisions.

This is why I think the person assigned POA needs to be present when the papers are signed and they sign that they understand what is involved in being a POA. Read the POA, is it immediate? If not then its "Springing" which means you only take over when she is found incompetent. If Mom is confident then she can do whatever she wants. POA does not mean your at the Principles beck and call either or that you are financially responsible for them. It just means she has named u as her representative when she is no longer competent to do so. And that means you only do what is written in the POA or how you think she would do something. Its a tool that is handy to have. Once she passes, the POA is no longer in effect.

And chances are the POA doesn't allow you to sell her stuff unless she's been declared incompetent and unable to use the stuff by two doctors.

Of course she can. She can also REMOVE YOU as her POA any time she wishes to if she is competent to do so. If your Mom is no longer competent and she is giving away her money from accounts then you should manage those accounts, giving her control over only small amounts of money at a time. She can, actually, not only sell stuff, she can GIVE IT AWAY.
I think you misunderstand the duties of a POA. A POA acts for an individual, to do what this individual wishes the POA to do while the individual is competent, and to act as the POA understands the individual would want him to when the individual is no longer competent, and in the best interests of the individual.
POA has power only so long as the person appointing them to act for them is wanted. The POA also must keep meticulous records.
If this elder is giving away or selling things, then you as POA should keep a record and diary (in pen in non-tear out composition book) daily of the actions of the individual who appointed you, to clearly document what was given to whom on what date. You could be liable for answering these questions in court should a step-daughter step in and say "Where is Mame's credenza?!?"
Sure wish you luck. If you no longer wish to serve as POA do document this as a resignation of duty by mail.
Wishing you luck. There is a lot of information online about the duties of a POA, and believe you me, it is MOSTLY duties, and not rights.

Yes. POA is only valid if mom has been declared incompetent.