Learn English – what does ask girl for hand mean

1. Azure-barred - Azure colored stripes in his body.

2. Does this paragraph describe the sex scene of Humber and Lolita but not after that?

This is the sex scene described and this is not the whole of it. This is describing the moments after having an orgasm.

3. Does this "when after having had my fill of her — after fabulous, insane exertions that left me limp and azure-barred" tell that they have finished making love or not?

As said in my above lines, they had orgasm and the scene after that is described here. Look at the lines saying -

all at once lust would swell again and the next moment the tenderness and the azure — all would be shattered.

This describes the start of yet another session of physical activity(sex). So they have not yet finished making love. Lets not disturb them.

In response to your question in comment:

First, Neon light will be RED in colour and Azure is related to the color blue. So they may be incorrect.

There are many reasons for getting stripes in body during intercourse one of which will be the nails scratching the skin but i don't get any idea of a blue colored stripe. (Maybe this is said for he is royal blooded. Author alone knows.)

And LIMP as an adjective here probably could mean Lacking in strength, firmness or resilience of his penis after orgasm(My Guess. Author's perspective might be different. But I'm sure.)

The words in the last line, 'would swell again' imply the erection he gets again.

They are just the description of the scene and the characters by the author.

Is it okay now?

“Making to” does mean roughly what you found in the dictionary. “She's making to run away” is mostly synonymous to “she's about to run away”. The difference is that “about to” indicates that she will run away in the future and doesn't convey how the narrator knows this, whereas “making to” tells us that the narrator sees something that shows that she intends to run away. She may be getting into a running stance, or distancing herself from the narrator. If she's “making to” run away, she might still change her mind, or be prevented from running away. That is, she is preparing to do it, but she might be interrupted either by internal reasons (change of mind) or external reasons (prevented) — in fact here it's a combination of the two (the narrator grabs her arm, and she doesn't really attempt to escape).