I don't know where the advice re airing cupboard came from. Tree paeonies germinate quicker with no heat. Yes, leave them to it. They are hardy. somewhere out of strong sunshine
pot them up in compost and put them outside somewhere.
In fashion atm. Much circulated on social media. Used by those who don't know (or don't care) about micro-organisms in the soil
I find seeds don't rot away in the weather.
If they are ripe/mature they will dry out and be fine. If they are not ripe, they will not ripen once removed from the plant.
i wouldn't remove, I'd be watching most carefully. Very interesting
they are delphs
If the photos don't load, make them smaller and start from the camera icon
Possibly Geranium nodosum
No harm but pointless as it's just the fruiting body of an underground network of mycelium. They're very short lived and you may not see those again for another year.