Improved Sorting

To achieve this you need to create a custom attribute for bestsellers and enable it for using in Sorting options: catalog > attributes > manage attributes

Product with values set in the custom attributes will be shown on the top of the list, while the remaining products will be sorted based on actual data. Please see more details on how to create custom attributes for bestsellers and most viewed options in our User Guide on Product Sorting.

Yes, it’s possible. To achieve that you need to navigate to system > configuration > catalog > catalog > frontend and select the necessary Sorting option in the ‘Product Listing Sort by’ field:

Yes, this can be configured in the Category Display Settings. Please navigate to Catalog > Manage Categories, select necessary Category from the category tree, open the Display Settings tab, uncheck the ‘Use Config Settings’ checkbox and choose the sorting option you’d like to set up as default for this category in the ‘Default Product Listing Sort By’ field:

To change sorting options display name as well as any other extension texts when using the Improved Sorting please open the file app\locale\en_US\Amasty_Sorting.csv

Add, for example line,

"New", "New In"

and refresh the cache.

To change the default wording (price, brand) you may use

1) app\locale\en_US\Mage_Catalog.csv will change all occurrences, not sure it's applicable in that case

2) open admin > catalog > attributes > manage attributes > and set appropriate store labels

3) use inline translation tool (not recommended, as it will be hard to find the translation when you need to change it)

It means there is a conflict with another 3-d party extension you might be using, please contact us and send temporary FTP and admin access details to us so we could fix the issue. 

Please open file app/code/community/TBT/Bss/etc/config.xml

and remove the lines:

<catalog>
<rewrite>          <product_list_toolbar>TBT_Bss_Block_Catalog_Product_List_Toolbar</product_list_toolbar>
</rewrite>
</catalog>

Please do the following:

1) Open app/code/local/MageWorx/SeoSuite/Block/Catalog/Product/List/Toolbar.php

2) Replace 
extends Mage_Catalog_Block_Product_List_Toolbar
with
extends Amasty_Sorting_Block_Catalog_Product_List_Toolbar

A Position sorting option is available in default Magento functionality and in the backend it is called ‘Best Value’. Position can be set on the product grid on the category management page.

Note that configurable and bundle products are composite and their quantity is 0. That is why sorting by quantity is not supported for them. The option ‘Use qty to determine if the product is `Out of Stock`’ doesn’t work for configurable and bundle product types as well for the same reason.

In case if sorting doesn't work there might be a conflict with other extensions. We have worked out a special tool for the case. Go to System>Configuration>Amasty Extensions>Extensions&Notifications>Troubleshooter, then find the Improved Sorting extension and click the 'Fix' button.
Providing that the issue hasn't been solved, send a request ticket to our support team.

Please check the extension settings highlighted on the screenshot below:

If you've enabled the option Use Index, you need to run re-index after changing the settings.

As for the reports, most likely your reports include data from completed orders for the bestsellers report while you haven’t excluded any other order states from Bestsellers.

Collect the information on how your bestsellers affect the sales level with the Advanced Reports module for Magento.