Two few questions

Would it be possible for only registered users to see the contact information?
Yes, with some customization using a membership plugin, but not just with GD.
You could also use some CSS, adjust as required:

.geodir_email {display: none}
.logged-in .geodir_email {display: initial}

Is it possible to change the style of the featured image of the Blog with Supreme Theme?
Probably depending what you mean, see https://wpgeodirectory.com/docs/customizing-your-style/

Thanks

I am not sure what you mean? All styling is just done with CSS as explained in the link I posted earlier, you can do that with the free version.

If you have any questions, give as much detail as you can together with links to the pages, and we will answer what we can.

Thanks

You will need to get a third party membership plugin, GD does not have a membership plugin.

Thanks