context free grammar accepted and generated language problems I'm having problems completing the following questions, I am able to attempt them but don't know if they are correct. Any help would be much appreciated.
Answer the following questions for a context free grammar $G=(N,\Sigma,P,S)$, where $N,\Sigma, P, S$ represents the set of non-terminal symbols, the set of production rules, and start symbol, respectively. Let $N=(S, A, B), \Sigma = (a,b), P= (S\rightarrow aAa|bAb, A\rightarrow aAa|bAb|B, B\rightarrow aB|bB|\epsilon)$.
$(1)$ Give a derivation of string $baabab$ in $G$
$(2)$ Give the language $L(G)$ that is generated by $G$        
$(3)$ Give a context free grammar which generates the language $L(G)\cap(w  \epsilon \Sigma^*| |w|_a = 2n + 1, n\geq1, where |w|_a= 2n+1, n\geq 1)$ represents the number of occurrences of $a$ in $w$.

$(1)$ $S\rightarrow bAb, A\rightarrow baAab, A\rightarrow baBab, B\rightarrow baaBab, B\rightarrow baaBbab, B\rightarrow baa\epsilon bab, \rightarrow baabab $
$(2)$ The language generated by the CFG seems to be a and b recurring to various powers eg. $aabbaaabab$. im not sure exactly what the syntax is for writing this is, but have attempted with $((a^nb^m)^*|n,m \geq 0)$
$(3)$ For this question also im not sure about the syntax for writing the language accepted by both $L(G)$ and $|w|_a=2n+1$. The way i understand it it should accept recurring a and b's like from L(G) but the a's have to be amod2=1. The following CFG seems to generate the union of these two languages.
$(S\rightarrow a^3Aa^3|bAb)$
$(A\rightarrow a^2Aa^2|bAb|B)$ 
$(B\rightarrow aB|bB|\epsilon)$

$$S\rightarrow aAa|bAb\\
A\rightarrow aAa|bAb|B\\
 B\rightarrow aB|bB|\varepsilon$$
$(1)$  You want the word $baabab$ so $S\to bAb\to baAab\to baaBab\to baaBbab\to baabab$
