In the UML 2.5.1 specification under section 22 "Standard Profile", p. 721 of the PDF file, it says: "The Standard Profile specifies a set of predefined standard stereotypes. A conforming tool shall support all of the stereotypes in the Standard Profile."
While the intended meaning of these stereotypes is explained in very general terms in Table 22.1, I couldn't find any requirements for their implementation. While some of them are probably trivial to implement or enforce -- for example, a «Utility» class must have only static attributes and operations -- what about «Auxiliary» and «Focus»? Are these intended to be merely descriptive? Can they be specialized by other Profiles to provide more meaningful implementations and constraints?
The StandardProfile.xmi document has nothing but the structure as shown in the diagram at the top of the section.
Yes, most standard stereotypes do not have strict requirements. They are intended to standardize the vocabulary among UML modellers.
Yes, you may specialize them.