Yes, your H tags and links could differ from styling in template CSS. I need to change it on every new Joomla instalaltion, when i use K2. (i mean to adapt K2 categories to whole website)
Rest is OK, K2 doesnt impact other classes on website.
Second question is not about K2 or Joomla, depends what HTML editor you install and use. See on JED what are most and best reviewed.