Thank you as always for your help Toritoribe and Elizabeth.
After reading through the threads linked and your answers, I got the following summary: (Are they correct?)
For the思う and 思っている thing, both forms can be used for first/third person, just depending on the situation and thought. 思っている suggests a strong opinion of the speaker, which is probably why the textbook suggests to not use this with first person.
So to make彼女がきれいだと思っている less ambiguous, I can change it to:
私は彼女がきれいだと思う。For "I think she is pretty."
彼女はきれいだと思っている。 For "She thinks X is pretty."
Useたい/ほしい for first/second person and たがっている/ほしがっている for second/third person.
However, たがっている/ほしがっている has a slight negative connotation and should not be used with strangers. Instead, we can use the たい/ほしい form, follow by forms such as という、ようだ、そうだ、らしい、などなど, those that suggest you heard/seen it from themselves or another source.
For the particles used to mark object desired:
を forたがっている/ほしがっている, since these are both technically verbs and take on a direct object.
を forたい, suggesting a weaker desire.
がfor たい/ほしい. In case ofたい, suggests a stronger desire.
So in the examples of:
お寿司を食べたい。<=Weaker desire
お寿司が食べたい。<=Stronger desire
お寿司がほしい。<= Where would this go? Or is it not comparable, since you just want the sushi and not to want to eat it?
For the が/はusage in subordinate clauses:
If it's an adjectival clause (modifying noun), the subject should be marked with が. がcan be replaced withの if the word after が is a verb or adjective that then modifies a noun.
But what would be the difference between:
私が読んだ本
私の読んだ本
If it's an adverbial clause (modifying verb), the subject can be marked with は.
I didn't quite get what you meant by はtend to cover the whole sentence… ?
が can be used if something is mentioned for the first time and that something isn't a noun like 私、彼、これ、等々(I'll call these general nouns for the next part…).
が emphasizes the clause/word in front of it if the clause/word is a general noun or something that's already mentioned, whereas はemphasize the clause/word after it. はis neutral when used with general nouns.
These are the very general ideas I think I got from reading the other threads… are these anything close to reality? I understand there's probably exceptions to everything, but are these at least close?
PS: The difference between written and spoken Japanese… is it generally that writing is more formal? What about in informal writings like journals/diaries? Would you use words like よ、ね、けどin informal writing? Also (this has been on my mind for a while now…) but is it in speaking or writing that you drop だ(the copula) if it's the last syllable?
I apologize for the super long post!