Identify the subject, verb, compliment and prepositional phrase

1. Arizonia is, therefore, an active battelfield in the war against the removal of these endangered species.
2. Authorized dealers must give purchasers permit tags as proof of legal sale.
3. What a thorny problem cactus rustling has become.
4. Many work at night and sometimes use permit tags over and over.
5. If you purchase a large cactus, always examine it for bruises.
6. A legally harvested cactus should not show any damage.

1. Ariziona-sub, is-v, therefore-comp, in the war against, of these endangered species-pp
2, dealers-sub, must give-v, purchasers-comp, as proof of legal sale-pp
3. rustling-sub, has become-v, problem, comp
4. many- sub, work-v, at night, over and over-pp
5. always, sub, examine-v, for bruises, if you purchase-pp
6. cactus-sub, should not-v, show-comp, any damages-pp

In grammar, it's complement, not compliment. A complement completes the subject (or is the same as the subject).

http://www.chompchomp.com/terms/subjectcomplement.htm

And apparently your text/teacher doesn't want you to identify direct objects, right? They are not to be confused with complements. Read carefully -- http://www.chompchomp.com/terms/directobject.htm -- especially the section called Don't mistake a direct object for a subject complement.

1. Subject and verb are correct; one pp is correct. All the rest is incorrect.

I'll re-do #1 for you, but you need to do LOTS more studying before trying this whole set of sentences again.

Arizonia - subject
is - verb
battlefield - subject complement
in the war - pp
against the removal - pp
of these endangered species - pp

1. Subject: Arizonia

Verb: is
Compliment: an active battlefield
Prepositional Phrase: in the war against the removal of these endangered species

2. Subject: Authorized dealers
Verb: must give
Compliment: purchasers
Prepositional Phrase: as proof of legal sale

3. Subject: cactus rustling
Verb: has become
Compliment: a thorny problem

4. Subject: Many
Verb: work
Prepositional Phrase: at night, over and over

5. Subject: You
Verb: examine
Prepositional Phrase: for bruises, if you purchase

6. Subject: A legally harvested cactus
Verb: should not show
Compliment: any damage.

1. Subject: Arizona

Verb: is
Complement: an active battlefield
Prepositional Phrase: in the war against the removal of these endangered species

2. Subject: Authorized dealers
Verb: must give
Complement: purchasers
Prepositional Phrase: as proof of legal sale

3. Subject: Cactus rustling
Verb: has become
Complement: a thorny problem
(No prepositional phrase in this sentence)

4. Subject: Many
Verb: work
Complement: (No explicit complement in this sentence)
Prepositional Phrase: at night, over and over

5. Subject: You (implied)
Verb: examine
Complement: it (referring to the cactus)
Prepositional Phrase: for bruises, if you purchase

6. Subject: A legally harvested cactus
Verb: should not show
Complement: any damage
Prepositional Phrase: (No prepositional phrase in this sentence)