Featured images in the sticky posts slider are 290 in height with a flexible width (maximum width is 640).
All other featured images are 290 width, and 290 in height. These images are displayed on displayed on posts on the home page, on archive pages, and on the search results page.
a) You didn’t make a mistake: the PHP of the theme specifies 290 max width and 290 max height, but the block that contains them is set as a percentage of the main column width in the CSS of the theme, and this percentage shrinks the featured images to maximum 280.
b) Since the maximum dimensions are set in the PHP of the theme, you can’t change them via CSS editing. So yes, if you want complete instead of cropped featured images on the front page, you need to downsize them to 280px wide before uploading them.