Is Shylock's conversion sincere? What evidence does the play offer in support of this?
Well, that one is up to the actor and the director, I think. I've never seen a production which tried to play Shylock's ''conversion'' at the end of the play as genuine, though I suppose it could actually be done.
Yet I'd argue that the text is fairly clear about its attitude to Shylock's conversion. Here's the bit of the text:
Two things provided more,—that for this favour,
He presently become a Christian;
The other, that he do record a gift,
Here in the court, of all he dies possess'd,
Unto his son Lorenzo and his daughter.
He shall do this; or else I do recant
The pardon that I late pronounced here.
Art thou contented, Jew? what dost thou say?
I am content.
Clerk, draw a deed of gift.
I pray you give me leave to go from hence:
I am not well; send the deed after me,
And I will sign it.
That's the last thing Shylock says in the whole play. 'And I will sign it'. Not 'gladly', or 'willingly'. But just that he's going to sign it. He'll do it. And notice the stilted, staccato nature of his speech: every single word he says is a monosyllable. His answers are short, sharp, and shocked, I think.
It's not the words of someone who has just undergone a major joyful conversion to Christianity. It's forced by the court (see above), and it's a legal requirement. He knows he's been beaten, and it breaks him. Because if there's one thing Shylock is clear about in the play is that he is a devout Jew, and that he respects his religion and his race. And even that, now, has been taken from him.
Hope it helps!