Were the Fang Gang wrong to let Illyria pretend to be Fred to her parents in 'The Girl in Question'?
About her dying I agree but nothing else I believe.
I think that that episode was meant to give the first hint that, despite what Angel and the rest had been told, Fred was, in fact, not totally, permanently lost. I have heard from several sources that, had there been a Season 6, he planned to split Fred and Illyria into two separate and independent beings, whether as a Jekyll/Hyde, Ben/Glory split identity, or as two actual people. We've seen the former in Season 10, so that would tend to give credence to te statement.
As for Illyria actually imitating Fred, probably it was like her rescuing Gunn from the alternate dimension, just her way of demonstrating her power. (This was, I think, after she had been weakened, so she would have wanted to demonstrate that, though not up to let former level, she was still formidable)
Think that would have been a great thing to explore.