To synchronize the product data correctly, you need to associate the 3rd Party Items imported from the particular eBay site with the related Magento Store Views.
Check the steps to insert images into the Custom Description.
Check the article if you need to specify a VAT Rate on eBay via M2E Pro.
If you want to list a product on eBay but make it unavailable in Magento store, you need to edit Product information in Magento.
If you want to set eBay store category from custom attribute, you should perform next...