Separation of slider image and featured and recent post thumbnail image

is necessary to add Activello child theme to solve the problems with images?

Yes to implement that solution you have to use the child theme that contains custom code.

And if answer is yes, is it activello-child 121 good enough?

No you have to use the colorlib-child-theme-38.zip shared in the following topic that contains custom code to achieve this functionality.

https://colorlibsupport.com/t/using-pages-rather-than-posts-for-flexslider/