Do all molecules in a compound have to be the same?

Answer 1

Yes and no. All molecules of a compound will have the same chemical formula, but some compounds have isomeric forms where the molecules can have different structures/shapes. These isomeric forms do sometimes have different properties than the usual form of the compound (e.g. boiling point, freezing point, rotation of polarized light) but they are still the same compound.

Answer 2

Yes and no, but almost entirely yes.

In general, if you're in a high school or freshman-level college course, "all the molecules in a compound have to be the same" is a fairly safe statement to agree with; if the molecules aren't the same, it's not a "compound," it's a mixture. Even if the molecules are isomers or stereoisomers or enantiomers, it's still a mixture (the term "racemic mixture" is sometimes used specifically for a mixture of enantiomers).

There are a few exceptions such as tautomers (molecules that can essentially "react internally with themselves" to form one of two or more different structures, typically with the only difference being the placement of hydrogen atoms, sometimes with double bonds or formal charges shifting to adjust valences as necessary). Tautomeric compounds exist as a mixture of these tautomer structures, constantly interconverting to remain in equilibrium. However, unless you're working in a field intimately related to chemistry, or at least taking an advanced course in it, you probably don't need to worry too much about these.