Interpretation of this regular expression: (1*0*)* Do the values of the two * inside the ( ) need to remain unchanged for every repetition of ( )?

For example, 110011001100 is part of this language set, but 1100100010 isn't?

Or can the values of the two * change for every repetition of the ( )?
For any two words $w_1$ and $w_2$, the regular expression $\texttt{((}w_1\texttt{)*(}w_2\texttt{)*)*}$ is equivalent to $\texttt{(}w_1\texttt{|}w_2\texttt{)*}$. Hence, both your examples are elements of the language generated by $\texttt{(1*0*)*}$.

In this setting, it is impossible to specify $w_1$ and $w_2$ occur equally often with a regular expression (except for a finite number of possibilities). Otherwise, you would be able to generate a non-regular language, in this case $\{ 1^n 0^n \mid n \in \mathbb{N} \}^\ast$.