Thanks for the questions, this is a save started directly from the tutorial and the house wasn't from the gallery. I think you may be right in that something glitched after the tutorial, although I remember completing it.
I've just discovered another bug with this save, and that is I only got Seasons last week (so this save didn't start out with Seasons) and I just realised that the weather is always "partly cloudy" and "warm" and there is never any rain or snow despite the seasons changing. Took me a while to realise as the trees still change and I had a thermostat installed so assumed that was the cause for the missing weather-related moodlets with my sims. This happened with other households too.
I started a whole new game and I was asked for the first time since I installed Seasons which season I wanted to start with. I started in winter & I finally saw snow and cold weather. I see this has happened to others playing old saves with a new Seasons install, although they seemed to still get rain & snow, just no related moodlets.
I've saved the "no mail" household to my library & started a whole new game (moving the household & existing lot back from my library) and this solved the Seasons bug for this household - they were finally wearing cold weather clothing for the first time! I'm not sure yet if it's solved the mail issue as I just played at ultraspeed for a few sim days but didn't see the mail person deliver mail.
I'll go back to my normal style of play and update this when mail is delivered (or not).