A friend of mine found out she was carrying twins very early on - 6 or 7 weeks, I think, so wayyy before she was showing. She found out she was pregnant, started bleeding a few days later, thought she was miscarrying, went in to get checked out - and not only was the heartbeat there, so was the other heartbeat.
On one pregnancy we found out the sex at the 20-week anomaly scan. On the other one, I remember one of the early scans checking for sex (12 weeks, maybe?) and not being able to tell because the baby was in the wrong position. I don’t know how sure they would have been otherwise.
When people show varies hugely. The standard wisdom is that fat women and tall women show later - but I’m not fat, I’m downright short, and I didn’t show till around 6 months either time. (Then in the ninth month I turned into a beach ball with a head.)
The due-date thing does sound weird. On both of my pregnancies, the early scans gave a very specific gestational age (like ‘8 weeks 3 days, +/- 5 days’ type of thing), so even if I’d had no clue about my last period, they could have estimated the due date to within a week or so. As far as I know, later in the pregnancy it’s harder to be accurate, but early development is very predictable. But it’s possible that she just doesn’t want to tell anyone the due date. Some people are weird about that. And with twins, the due date is even less likely to have any relationship to when the babies actually arrive, so more reason not to tell people.