what is your spacing set you. there should be only one separation layer and horizontal should be maybe .3 to .5. other than that you need to increase support density. use 50% or higher if it has to look nicer. remember that no matter what you will not have a perfect surface under your supports because of that i layer gap but that has to be there for removal. to get a perfect surface you need 100% support with a zero layer spacing and then use dissolvable supports
Yep, you should reduce the spacing because the 0.3mm can cause especially on curves that the filament doesn't stick the the support material and then it choses the "shortest way" which is a straight line
Are you just using one layer for the skin? It's hard to tell in your pic, but is the support material you can see through the gaps? So your problem is on the exterior, not on the interior? A second/third perimeter skin will help.