Hi,
1. You can find order statuses via the menu System>Order statuses. And there are many settings where you can configure what order status should apply/be taken into account for a specific action. Most of them are located in the "order" section of the HikaShop configuration.
2. If you activate the "Payment of orders not paid immediately" setting of the HikaShop configuration yes.
3. It depends how you configured the settings of the order section. Mostly, you'll have the stock of the product of the order decremented.
Also, if you have reports based on statuses, the reports might change. Etc...