I suppose that it is natural to use “past” with “midnight” and “hour” if minutes are more than 30, but it will sound unusual when used with a number like “41 minutes past 5”?

Both sound natural to me.

In your first example it sounds more formal than "twelve forty-eight am". I wouldn't say it in casual conversation, but in a news article like this it fits.

In your second example that is the only good way to phrase it. You could say, "at twelve forty-one, one forty-one, two forty-one..." but that's awful. If it was a single time I would just say "five forty-one".

Depends on the dialect of English.

Some would switch to saying "before" or "until (typically shortened as 'til)" while others would keep saying "past" or "after"

Ie: 19 minutes til 6 = 41 minutes past 5

Most speakers in either dialect may omit "minutes" in conversation because it is implied.

There are of course other dialects where neither seems natural and the time will just be given as a single number, ie: "it's 5:41"

I've largely heard the first two used more commonly in UK English and the latter used more in American English.

I think it's rare that times will be given with such specificity, so that might be why it automatically sounds a little unusual.
But apart from that I think "five fourty-one" "41 minutes past 5" both sound equally normal to me (who is a non-native though)