Here's the Greeκ text:
πᾶς που γιγνόμενος πρεσβύτερος ὄκνου πρὸς τὰς [665ε] ᾠδὰς μεστός, καὶ χαίρει τε ἧττον πράττων τοῦτο καὶ ἀνάγκης γιγνομένης αἰσχύνοιτ᾽ ἂν μᾶλλον, ὅσῳ πρεσβύτερος καὶ σωφρονέστερος γίγνεται, τόσῳ μᾶλλον. ἆρ᾽ οὐχ οὕτως;
1) Why is χαίρει indicative but αἰσχύνοιτ᾽ optative?
The genitive absolute ἀνάγκης γιγνομένης functions as the protasis of a future less vivid condition, requiring an optative in the apodosis.
2) Why is μᾶλλον repeated twice?
It's eliptical for τόσῳ αἰσχύνοιτ᾽ ἂν μᾶλλον, "he would become more ashamed, by as much as he becomes older and wiser, by so much (he would become ashamed) more."
{ οὗτοι οἱ λόγοι Ἑλληνιστί
πᾶς που γιγνόμενος πρεσβύτερος ὄκνου πρὸς τὰς [665ε] ᾠδὰς μεστός, καὶ χαίρει τε ἧττον πράττων τοῦτο καὶ ἀνάγκης γιγνομένης αἰσχύνοιτ᾽ ἂν μᾶλλον, ὅσῳ πρεσβύτερος καὶ σωφρονέστερος γίγνεται, τόσῳ μᾶλλον. ἆρ᾽ οὐχ οὕτως;
1) Why is χαίρει indicative but αἰσχύνοιτ᾽ optative?
ἡ γενικὴ μετοχὴ «ἀνάγκης γιγνομένης» ἐστιν πρότασις καὶ τὸ «αἰσχύνοιτ᾽ ἂν» ἐστιν εὐτικὴ ἀπόδοσις.
2)Why is μᾶλλον repeated twice?
Τοῦτό ἐστιν ἔλλειψις ἀντὶ τοῦ « αἰσχύνοιτ᾽ ἂν μᾶλλον» }
I am writing in Ancient Greek not because I know Greek well, but because I hope that it will improve my fluency in reading. I got the idea for this from Adrianus over on the Latin forum here at Textkit.