As you mention, it's your own choice; I see the crux of this matter in two points: the first is how you accumulate your theta and the second is how good your volatilities on Friday look versus on Monday.
I'd personally be inclined to use calendar days for something like oil (I would expect that the chance of a geopolitical event such as a war starting over the weekend is at least 2/7th), while for something like cotton I'd be more inclined to use business days.
During the day: I have never bothered with this, but I guess if you're looking to be a market maker you should. The thing here is that not all hours are equal. If you look at intraday measures of realized volatility, you'll see that around the pit opening and around settle are typically more volatile than other hours in between. So ideally you would account for that. Additionally, on days on which numbers are published, you would also expect some potential additional volatility around them for which you could adjust. So I wouldn't use either or what you are suggesting if you want to be really precise about this.