How do I fix a sidebar category list?

I am working on a GridMarket-MarketPress multisite. I have a sidebar Global Product category list that is not behaving as in my Product Edit pages.

1) I am not indenting sidebar global categories properly (can css help this).

Sub-categories do not indent under parent category, instead they order by name all-together underneath each other which is confusing.

2) Possible theme glitch may not refresh category name edits, everywhere in a site.

The parent category name, whose old-name still shows up in the sidebar and post-title for the page, only shows correctly in page category list options.

Thread showing graphics of my sidebar and page: https://premium.wpmudev.org/forums/topic/how-do-i-edit-the-format-of-the-gridmarket-side-bar-category-list#post-534812

Thread started a year ago outlines my ultimate goals: https://premium.wpmudev.org/forums/topic/sidebar-categories.

Thank you.