Great, problem fixed. For the benefit of other users here comes the code I added to my custom.css stylesheet:
/* Hide alternative text field for intro pic */
#jform_images_image_intro_alt {display: none;}
#jform_images_image_intro_alt-lbl {display: none;}
/* Hide alternative text field for main pic */
#jform_images_image_fulltext_alt {display: none;}
#jform_images_image_fulltext_alt-lbl {display: none;}
/* Hide caption setting for intro pic */
#jform_images_image_intro_caption-lbl {display: none;}
#jform_images_image_intro_caption {display: none;}
/* Hide float setting for intro pic */
#jform_images_float_intro-lbl {display: none;}
#jform_images_float_intro_chzn {display: none;}
/* Hide float setting for main pic */
#jform_images_float_fulltext-lbl {display: none;}
#jform_images_float_fulltext_chzn {display: none;}
I still think EL should add a tab for their intropic and mainpic fields with tickboxes allowing userse to make those items invisible on the images tab.