Sometimes when I insert an image into a post, it doesn’t show on the Home Page like it should, but only shows in the Post page. Are you supposed to insert the image in “Visual” or “Text” mode in the editor, in The Columnist Theme?
“Visual” or “Text” means you see the images or you see their code. It doesn’t make a difference as far as inserting images is concerned: the Add Media tool is common to both.
Suburbia and the Columnist work the same way: an image you insert in a post will show on the front page if it’s the first image you upload from your computer via the Add Media tool of that post, or if you set it as a featured image to that post. It won’t show if you insert a previously uploaded image by selecting it from your media library, or if you insert an image hosted elsewhere.