FB Share and Like

FB Like and share counter is working with the plugin or not.

other social sharing option is available or not.

Yes FB Like and share is available.
You can activate it in “Edit options”:
https://www.screencast.com/t/TR1GANyCay

Here an example how it works
https://www.contest-gallery.com/voting-types/#!gallery/139/image/10432/20200317_ASG%20IG%20photo_01__littlemsfoodie_LobsterTaglerini

Other social sharing options are not available.

is there any option for custom cover photo for sharing on FB.

No, that is not possible.