For the SKU search problem:
We will explain in detail. When you add the sku value on search form field, it will be redirected the single product page.
While ajax searching, if you click the "enter", default search form query will be worked and you can see the non-result page.
Because default search query has no sku parameter search feature.
It just searches the product titles or slugs. So for the sku search, ajax search function will redirect you to the single product page. You needn't to press "Enter Key".
For the other problem:
Which browser did you test? We checked it on firefox browser and everything is shown correctly.
Please let us know in detail again.
Best Regards, C-Themes