The generate_header_items() function has been simplified: https://gist.github.com/generatepress/4cfa628cec96088dcbf8dd8cf399b83e
Simply rearrange the order as you need it.
The icon thing is most likely because you’re using tables to display images and content. Tables should only be used to display tabular data.
Instead, try using a plugin like this: https://wordpress.org/plugins/lightweight-grid-columns/