Hello Daniel,
1. To widen the sub menu background you can insert the following code into Appearance > Customizer > Live CSS:
.sf-menu ul{width:15em;}
You mean that you would like to place the arrow next to the categories that have sub categories?
2. Unfortunately there isn’t a way to display the date and time in the widget’s main post, as you can see, they are displayed above the post description.
3. You can start by adding the following code in Live CSS:
@media (max-width:768px) {
button.navbar-toggle.visible-xs:before {content: 'menu';}}4. Unfortunately you can’t insert an image but you can use a different icon from https://fortawesome.github.io/Font-Awesome/.
You can insert the icon’s unicode in this code:
.format-standard.grid-item .entry-meta:before {content: '\f15c';}