The first is that when within a product you click on next or previous, social icons disappear
The second is that when you add more than one product (for example two) to cart, if you try to delete one of them is not refreshed and disappears, when there is just one works fine
I do have the second issue - items not deleting from cart module. Well, they do delete in the system, but the cart module does not update.
It is fine on the checkout page.
I am running VM 3.0.6.2 and Cleanmart 3.2
A quick fix for now is simply to set the module not to show the remove icon (in module settings). Buyers can remove by clicking "view cart" and then remove from there
About "social media icon" disappearing. Are you using CleanMArt v3.2 and did update the dynupdate.js file as it was explained in the Release_Notes.txt ?
because there is no Facebook Like box on your website, since the like box is not exist; this line causes error and JavaScript stops working starting from that line (right after the Facebook line, there is the line to re-load the AddThis social media icons)