I’m not sure who you mean by TT. Waze does take a limited amount of traffic speed data from Google, but only for roads where Waze isn’t getting enough data from Waze users and Google does have decent information. Although Google bought Waze a couple of years ago, Waze is still run as an independent company and the relationship between the two is more of a limited partnership where the two share some information.
The routing servers can take account of Waze users driving through closures. If several users are seen doing this, the routing servers will start routing through the closure, until it either ends or a period with no wazers is seen. It does take a few Wazers to enable routing through a closure.
But consider this: nearly all Waze users will be using routing (as opposed to just driving with Waze running) and Waze will be directing them around the closure. And most of them will believe Waze and take the diversion! And since Waze may well pick a diversion route that leaves the M3 much earlier than the “official” diversion route (which may be choked by traffic), they won’t get close enough to see that the closure has ended early.
As for using smaller B roads - yes Waze does have a tendency to do this more than people might think. Although Waze will give preference to “higher” road types, this isn’t done in a simple manner. For any route, the beginning & end of the route will consider all road types. The middle of the route will prefer higher road types - and the longer the route, the more strict this is. So for a (say) 200 mile route, most of the route will very strongly prefer motorways.
Now if you’re on the motorway and Waze sees a significant delay building up, it will see if it can re-route you. Since this is effectively a new route, it will now consider smaller roads at the start of it - so may take you off via smaller roads to get to the next junction because it looks quicker. Exactly this happened to me last week. I was heading west on the A12, expecting to turn onto the M25 and take the Dartford Crossing. About 3 miles from the M25, traffic was at a standstill and Waze re-routed, telling me to go past the M25. The jam was entirely caused by a tailback of traffic trying to turn left onto the M25. Instead, Waze took me further into London on the A12, then south through residential streets to the A127, then back out of London to the M25, where I was able to join and head towards Dartford - and all without stopping for anything except traffic lights.
The last thing I will mention about the Waze routing is “predictability”. Despite the app offering a “fastest” route option, that isn’t quite true. Traffic speeds can sometimes be very variable and if Waze always chose just the fastest segments, arrival times would change too much and wouldn’t be so reliable. So Waze also has a minor preference for predictable routes: things like fewer turns or less variation in traffic speed. If the motorway is starting to show sudden, unexpected slowdowns, then a minor route on which traffic is moving smoothly may be preferred - even if the time saving appears small.