One thing to keep in mind in all questions about "what's right and what's not?" is that conventions don't always matter as much as one would think.
When a trader marks his vols by looking up option prices on the market, he is going to mark them using the pricing model which his quants implemented. So whether he uses one convention or the other, he's still going to get the same price for these options and most likely similar prices for other options.
Now, to answer your question, when it comes to time conventions, neither calendar nor business days are really correct. If you use calendar days then your options will have 3 days time decay on Monday which you can't do anything against. And yet in some cases one can think that the market moves more between Fri close and Mon close than other days so biz days would not be appropriate either.
What some desks, especially in equities implement is an elastic time. That means they weight time depending on much they believe the market will move relative to other days. So for instance any day with foreseeable volatility due to some number announcements (results or nonfarm payroll) will have a heavier weight. That means that on these days your options will have more decay, which is fair given that the market is expected to move more as well. However these are very subtle considerations for large volume market-making desks.
Regarding expiry date
It is customary to model the option as equal to the intrinsic value on the day of expiry. Risk managing expiring options is a known headache, and again this is usually done by market-making specialists. Most options traders will avoid having options expiring in their books which are too close to the strike, and if they have them they will have to do a lot of adhoc delta hedging.