Hi,
1. That's possible with our integration with AcyMailing. You can configure marketing campaigns in AcyMailing with triggers when an order is created, confirmed, add delays, etc. That's why we didn't do anything for that directly in HikaShop since AcyMailing already does a really good job on the email marketing side and covers everything we could possibly do.
2. The characteristics themselves on the product edition page are already drag n droppable for their ordering.
So I suppose that you're talking about the values of the characteristics, when you edit the characteristics.
That's indeed a good idea. We actually want to redo the characteristic edition interface in the future in order for it to be more user friendly.
3. Isn't there already the number of products displayed ? For example:
monosnap.com/file/olXnaEypvfnRUHgwfKSHYVn43urH3G
Now having a cart icon could be interesting but you can already easily add the icon you want to it with a bit of CSS.