Rein here from Shopify. As I understand it you are looking to create a community section of your site whereby customers can chat, save products and send messages to one another. This is not something that would be possible out of the box.
There are various apps that you could combine to get an effect similar to this however knowing which would not cause conflicts would be tricky. Therefore the best recommendation here would be to work with a Shopify Expert. Shopify Experts are vetted community members who excel in design, support, marketing and programming for a cost. You can check the marketplace here and see if you can work with a developer who can get this setup for you.
Have you taken a look at any other avenues to accomplish this? - Rein
That is a fair point. Most apps would not leave a footprint, but something as fundamental as adding a whole forum and messaging system would be a bit more than an app could manage in most cases.
My suggestion for working with an experienced Shopify Expert would be the best in this case, if you are not sure how to proceed directly.