Hi,
Regarding the add to cart issue, that's because your cart module is inside your product page. So the form of the cart is inside the form of the product page and that's not possible in HTML. That's why it doesn't work properly.
Instead of adding your cart module inside your product page, you should add it to your template's right side position.
So as Mohamed guessed, it's probably coming from a view file edition that you did to add the cart module in the product page.
Regarding the UPS error, it means that the weight/dimensions of your products or the way you configured the UPS plugin is not correct.
Regarding the error during the install, turn off the debug mode option of the joomla configuration before trying again and it should work fine.