I don't have the time for a very in-depth answer at the moment. However, if you look at P-29.6 of the 2013 Blue Book, you can see what they italicise and what they don't. (Just do a Ctrl-F for the relevant words.)
https://iupac.qmul.ac.uk/BlueBook/P2.html#2906
- sec-butyl is italicised
- tert-butyl is italicised
- tert-pentyl is italicised
- o-tolyl is italicised
- isopropyl is not italicised
- isobutyl is not italicised
- neopentyl is not italicised
It should be pointed out that of all these, only tert-butyl is a preferred prefix. The section linked above makes this clear. But in most cases, that probably needn't concern you.
As for abbreviations, these are covered in the 2008 IUPAC recommendations on Graphical Representation Standards for Chemical Structure Diagrams. See in particular Table II on page 406, which gives the following forms: iPr, iBu, s-Bu, and t-Bu (which is in line with the Blue Book). It says that if you choose these abbreviations, then explicitly defining them is unnecessary.
(Of course, you can choose whatever abbreviation you like, as long as you define it. The text accompanying Table II makes that clear. It also says that the non-italicised forms are fine too.)
Authors are welcome to create their own abbreviations as well, but any abbreviations not included in the list below should be defined clearly when they are used. [...]
Several of the abbreviations listed below include portions of the text in italics. The italicization shown is the preferred formatting of those abbreviations. However, the corresponding forms without italicization are also acceptable.
