Adjectival infinitive or infinitive of purpose

Hell, everyone,

About the function of infinitive phrases, I would classify them as follows;

1) “I will buy a new coat to wear in winter.”; without ‘it’, “to wear” is an adjectival infinitive to modify “a new coat“.
2) “I will buy a new coat to wear <it> in winter.”; with ‘it’, “to wear” is an infinitive of purpose.
3) “He's saving money to buy a flat.”; this case is ambiguous, so “to buy“ can be either an adjectival infinitive or the one of purpose.
4) “He bought some flowers to give to his wife.”; this case is also ambiguous, so “to give” can be either an adjectival infinitive or the one of purpose (to answer “why?”).

However, above 3), 4) both have been classified as ‘infinitives of purpose’ only to answer “why?” in ‘Perfect-English-Grammar’ and ‘BBC, Learn English Council’ as follows;

https://www.perfect-english-grammar.com/infinitives-of-purpose.html
https://learnenglish.britishcouncil.org/english-grammar-reference/to-infinitives

Thus, my question is,

1. about above 1), 2), adding ‘it, them’ (which relates back the preceding noun) or not can be a critical factor which can decide the function of infinitive phrases, while in 4) there is no ‘them’(= some flowers) in “to give to his wife”?

2. Do you agree with my classification for above four examples?

Would hope to hear,