Hello. Thank you for attaching the file with your questions. Yes, you must follow the rules of the Chemistry Code for this table in Appendix 3. If the book is not using Chemistry Code in the entire transcription, you simply state that you are following that code for this Appendix 3.
Chemical SYMBOLS are not treated like braille abbreviations nor are they treated like braille single letters. For example, N for nitrogen is simply "cap n" and is punctuated mathematically. The SYMBOLS are not treated differently within narrative. In other words, do NOT use an English letter indicator for the SYMBOL N for nitrogen. Read Section 3.5 in the Chem Code. Two-letter chemical SYMBOLS always show the second letter in lowercase. If you see two capital letters in a row, such as CO, that is two elements -- carbon and oxygen -- "cap c cap o" with a dot 6 math comma--no spaces unless print shows a space.
Physical states (solid, liquid or aqueous, gas, crystalline) are in parentheses -- do not retain the italics, do not use English letter indicators. See Chem Code Sec.9.2 for a discussion of physical states.
Superscripts and subscripts follow the usual Nemeth Code rules. Follow print spacing for example S(rhombic) has no space (and no ELI). Same goes for P(white) and P(red).
Your question about g/mol is out of context and so I cannot give a definitive answer.
Scientific abbreviations in a chemistry transcription follow the rules of the Nemeth Code EXCEPT they are spaced as in print and they are punctuated mathematically. So .. g/mol uses an ELI for the g as long as there is a space before the g and as long as this is in the context of an abbreviation. If the g is an abbreviation and is unspaced from what precedes it, no ELI is needed. If g/mol is being used as a variable, no ELI is used. (Variables are usually printed in italics so they are easy to identify -- study the book to see how the printer has been identifying variables throughout.) Section 9 of the Chem Code covers abbreviations in a chemistry transcription in more detail.
The organic molecular formulae shown at the bottom of page 3 of your file are simple to do in Chem Code. You do not separate the letters. Section 4.1.3 of the Chem Code shows a simple molecular formula for benzene as an example. Your first formula: CH3COOH is straightforward cap c cap h Nemeth 3 cap c cap o cap o cap h, all unspaced, no subscript indicator for the numeral. Fun. It will be another matter formatting the wide table!
Take some time to learn what you are looking at, finding out what it is called, and then researching it in the Chemistry Code. Keep asking questions if you are uncertain.
Appendix 4 in the attached pdf document is back to math, not chemistry. The two functions you have pointed out follow rules of the Nemeth Code for functions (Rule XVII). Your specific question about dots 56 in "log B" is answered in Sec. 27.a of the Nemeth Code which is discussing nonuse of the English letter indicator: the letter B does not use an ELI. The letters A and B have individual identities in "Log AB" and so are individually capitalized.
I'm not familiar with the term "stuck symbol."