I can't choose certain attribute because it is not presented in the list

A list of attributes available for the selection in M2E Pro includes only Text Field / Price Type attributes which are presented in all Magento Attribute Sets. 

If you need a specific Magento Attribute in the Module, you should add it to all your Attribute Sets in Magento. To do it, please navigate to Catalog > Attributes > Manage Attribute Sets in Magento v1.x and Stores > Attributes > Attribute Sets in Magento v 2.x.

#product attribute