1. Is there a feature to allow users to login via facebook credentails? I would also like to show user profile photos from facebook both for the customers and the sellers.
Our module does not include this feature. but you can use 3rd party module to implement this.
Seller and customer share the same log in, so as long as the 3rd party module works for customer, it also works for sellers.
2. I would also like to add a RENT option along with the buy option for sellers when they list the item. Where can I customize it as the admin of the marketplace to allow for such option?
It depends on how you will implement this, at least I think you will need to add some new fields to product. you may need to modify the following files, but it is just a guidance.
override/classes/Product.php
override/controllers/admin/AdminProductsController.php
3. I would also like a seller and buyer native apps on ios and android. Are there any solutions or recommendation?
PrestaShop1.6x supports responsive theme design, so it should support mobile devices.
Our modules support mobile devices too, but we do not have any special APP for mobile devices.