Strange behavior running headless vs non-headless

I am observing three strange behaviors when running existing Keyword tests headless. I am not having these issues running non-headless.

1. There is a searchbar that restricts characters to 30 in the HTML (maxLength = "30"). This is seemingly ignored when running headless and more characters can be entered.
2. There is an export to file button that when clicked is not actually exporting the file to the Downloads folder
3. When running headless, TC/TE seemingly can't recognize the message on a browser alert/popup thus it can't be asserted. (I already have a post about this one: https://community.smartbear.com/t5/TestComplete-Questions/Browser-alert-popup-not-found-when-running-headless-no-issues/td-p/258299) 

Does anyone have any idea why this is happening or what can be done about it? 

Thanks