I am currently working on my Bachelors thesis with TexLive 2018 in TexStudio. My University demands the usage of the CiteThemRight reference styling, which is an adaption of the Harvard referencing standard. (This question is edited based on the discussion in the comments)
Here's how it looks right now:

Here's the current status with highlights and notes on what needs to change. Please note that the date added text should of course be in the same font and size as the rest, I just edited the picture badly.
This is how the literature is currently defined:
\usepackage[comma]{natbib}
\setcitestyle{aysep={,}}
\bibliographystyle{agsm}
I have found some questions, linked in this comment where @Mico's answers suggest changing the style defined in the agsm.bst (more, a copy thereof). I have tried to find my way in the file but cant make heads or tails with it. Thank you


natbibcitation management package is its control over the appearance of citation call-outs. Thenatbibpackage doesn't have much of a role in the way the bib entries are formatted. Which bibliography style do you use at present? – Mico Apr 09 '19 at 17:56\bibliographystyle{agsm}. Is that what you meant? – JFNT Apr 09 '19 at 18:02