Hi again,
As for these answers of yours:
The spoons I used at dinner are the same as (the spoons used by Jill) Jill's (at dinner). OK
I have the same book as (the book) Jane /or Jane's??? (has) Here, the sentence is equating 'I' to 'Jane'. Consider that 'I' and 'Jane' are the subjects of the two clauses.
Are you saying no. 1 can use both 'Jill' and 'Jill's'? No. The spoons I used at dinner are the same as Jill's (spoons). The sentence is equating spoons to spoons. 'Spoons are the subject in both parts of the statement.
The spoons I used at dinner are the same as (the spoons used) by Jill (at dinner) -- See 'are the same as by Jill' is not good. No. You are omitting too many words to make the meaning clear. You could say The spoons I used at dinner are the same as those used by Jill.
As to no. 2, which is correct?
I have the same book as (the book) Jane (has) The sentence is equating 'I' to 'Jane'. They are both subjects. Thus, I have the same book as Jane.
I have the same book as Jane's -- Although I couldn't construct a full sentence, I feel this is how people very often speak in everyday situations. Perhaps sometimes, but people do not always speak carefully. Do you?
Best wishes, Clive