$FNP$ ,$ \#P$,$\oplus P$ classes I was trying to understand these classes but always got confused ... the questions are : 

What is the relation between $FNP$ and $\#P$ , in particular is it an open question ?

What is the relation of $\oplus P$ and $NP$ ? is this question open ? 

What about the relationship between $PH$ and $P^{FNP}$ ? is this question open ?
1)$\bf FNP$ is contained in $\bf FPH$, which is called the "functional polynomial hierarchy", where every function in $\bf FPH$  is polynomial time 1-Turing reduciable to some function in $\bf \#P$. 
2)We know from the Valiant Vazirani theorem that $\bf NP$ $\subseteq$ $\bf RP^{PromiseUP}$. We also know that $\bf UP$ $\subseteq$ $\bf \oplus P$. Therefore, we have $\bf NP$ $\subseteq$ $\bf RP^{\bf \oplus P}$.