Hi,
Your 1st problem can't be solved with coding. It is a computer related issue, actually it is not an issue at all, this is how things are. If you click the BACK button of your browser, the website will be loaded almost immediately because it uses the "temporary internet files" that stored in your computer to show the page. But after clicking the refresh button. (this is why we have a "refresh" button, otherwise we won't need that button at all) the page will be rendered again from the server instead of using the local copy in your computer. Once the page is rendered again, the added product in the cart will show up.
Second question; this is a 3rd party extension to Virtuemart. Our templates/extensions are also 3rd party extensions to Virtuemart. 3rd party extension might not support each other, this is normal. Because we don't know what structure is being used.
Those developers have developed that add to cart effect to work with the official Virtuemart Shopping Cart module, but you are not using the official Virtuemart Shopping cart module anymore, you are using "our 3rd party Virtuemart Shopping Cart module". With a little coding modification in that plugin (plugin of that effect) the plugin will work within our Dropdown effect as well. But this is beyond our free support unfortunately. We don't provide free support for custom changes.
Regards.