Renas,
There's no way to disable the popup after the Like click. When user's fill that comment box in, it gives the Like a *much* wider publicity on that user's wall and their friends wall. If they don't fill it out, the Like still counts, but it's not as good for social promotion, just so you know.
As for the cutoff box, you'll need to modify your template a little to fix that. Please edit
/plugins/system/jat3/jat3/base-themes/default/css/layout.css
Around line 17 in the .column style definition, remove the overflow:hidden setting.
Hope that helps!
Alex