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 ? 
$FNP$ ,$ \#P$,$\oplus P$ classes
cc.complexity theory
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 $\bf NP$ $\subseteq$ $\bf RP^{\bf \oplus P}$.