Meaning of "he is trying to keep something alive." and "righteous set of Dexter's mouth..."

Question

This passage is from The Children's Bach by Helen Garner

‘Sing something,’ said Poppy to Elizabeth. ‘Sing ‘‘Breaking Up Is Hard To Do’’.’

‘Oh, not that,’ said Philip.

‘You do the come-ah come-ah,’ said Elizabeth to Philip.

They sang. Billy flung himself about in Dexter’s arms, loopy, with rolling eyes. Their rhythm was solid, they slid their eyes sideways to meet, and smiled as if to mock each other for their unerring harmonies. Athena saw they were professionals. The piano is such a lonely instrument, she thought: always by yourself with your back to the world. The music, thought Dexter irritably, is American music. He remembered Dr A.E. Floyd’s quavering voice on the radio: ‘Some people pronounce it Purcell: that’s an Ameddicanism.’ The song ended. ‘Now we’ll sing,’ said Dexter. He put down Billy, who wandered away; he made Arthur come and stand beside his chair, and they sang ‘The Wild Colonial Boy’. Arthur had the long song word-perfect. He stood to attention and threw back his head on the high notes. Vicki watched with a cold eye. ‘I suppose,’ thought Elizabeth, ‘that he is trying to keep something alive.’ It embarrassed her to see the righteous set of Dexter’s mouth between verses: she looked away.

Drunk on performance, Dexter hardly let a pause fall before he cried, ‘And now I’ll sing ‘‘When I Survey the Wondrous Cross’’ . . . And pour contempt on awhaw-hawl my pride,’ he bawled. He drew breath and looked around him, smiling, with tear-filled eyes, his right arm still extended in its melodramatic curve. No-one spoke. Poppy turned a page.

‘Mind if I sing another stanza?’ he said.

‘Yes,’ said Vicki. ‘I do. Hymns are boring.’

a)

Does "He is trying to keep something alive" mean:

1. He is trying to draw their attention toward himself?

2. He is trying to draw their attention toward something?

b)

Does "righteous set of Dexter's mouth between verses" mean "the posture of Dexter's mouth after reading each verse that seemed he was very satisfied of himself"?

c)

Does "Drunk on performance, Dexter hardly let a pause fall before he cried" mean:

1. Because he was drunk in performance, after he sang a song he cried immediately that he want to sing another song?

2. Because he was drunk in performance when he wanted to increase his voice during singing he could not fall pause before it?

I asked this question in literature Stack Exchange but nobody answered.

Answer 1

a) Literally, the sentence in a) means that Dexter is trying to preserve or maintain some circumstance or state of being. But that is pretty generic, and I don't think it is possible to determine from the quoted passage exactly what Elizabeth means. We would need to know more about Dexter, Elizabeth, possibly Arthur and other characters, and the story so far.

b) Yes, that seems about right to me.

c) "Drunk on performance" means that the experience of performing has put Dexter in an altered state of mind—one of excitement and reduced inhibition, similar to being drunk. It does not mean he is literally drunk while performing. The sentence means something like

Excited by the experience of performing, Dexter had barely finished singing when he called out ...