I agree on all points:
1) Benjamin Franklin proposed the turkey as the official bird of the United States rather than the bald eagle.
- B. F. = subject --
Yes- proposed = complex transitive verb --
Yes; I am not familiar with 'complex' here; do you mean the 'proposed as...rather than'?- the turkey = direct object --
Yes- as the ... eagle = object complement ? --
Yesis "as" a preposition here? --
Yes: 'I worked as a doctor'. 'The doctor, as a specialist, recognized all the symptoms.'2) I worked with him to gain some experience in the field.
- I = S --
Yes- worked = monotransitive verb ? --
Yes- with him = prepositional phrase; "him" object of the preposition "with" ? --
Yes- to gain....field = adverbial of purpose. --
Yes3) Her latest book is printed in colour. S V A(m) ? --
Yes- her latest book = S --
Yes- is printed = intransitive verb --
Yes- in colour = adverbial of manner --
Yes