1.)  We were going to find out [DO of "were... out" which blood types were 

compatible (PA)]. | To find this out we first learned the types (DO) {of blood}, O, AB, B, & A. |

     "Find out" here means "learn." (I would not, however, argue with someone who wanted to explain "out" as an adverb.)
    "To find this out" is an infinitive phrase in which "this" is the direct object of "find out." The phrase functions as an adverb to "learned."
    "O, AB, B, & A" are appositives to "types."

equals which blood (PN).] |

     Personally, I would consider the "up" as part of the verb here. "Looked up" means "found" or "determined." Again, however, I would have no trouble with considering the "up" an adverb to "looked." (It is not worth arguing about.) On the other hand, "up which" or "up which color" is not a prepositional phrase because "which" meaningfully goes with "color" and "color" is the subject of "equals." 
     Because "equals" here means "represents," some people may prefer to explain "blood" as a direct object. For those who want a clear "either/or" distinction, the arguments become complex and end up in questions of semantics and the philosophy of language. I would simply accept either.

that's chewing up some tree limbs (DO).] |

     "Chewing up" is equivalent to "devouring," but I would also accept "up" as an adverb to "chewing." On the other hand, "up some tree limbs" is not a prepositional phrase. To explain it that way is to suggest that the truck is up in the tree limbs.

(DO). | *You* Also, blow out the candle (DO) {before putting it away}. |

     "Take off" means "remove." "Off the lid" cannot be a prepositional phrase because the sentence means "Take the lid of the pumpkin off the pumpkin." That, in turn, suggests that in "take off" the "off" can be considered the preposition in an ellipsed prepositional phrase -- "Take {off the pumpkin} the lid {of the pumpkin}."
    Similarly, "blow out" means "extinguish," but "out" can be explained as an adverb to "blow." It does not make sense, however, to explain "out the candle" as a prepositional phrase. The sentence does not mean "to blow something out the candle."
    "Putting" is a gerund that functions as the object of the preposition "before." "It" is the direct object of "putting," and "away" is an adverb to "putting." 

{to the horse-lot} to look {at the horses}. |

      Although I would consider "down" to be an adverb to "drove," if a student identified "down to the horse-lot" as a prepositional phrase, I would simply accept it. 
     I vaguely remember a grammarian on the ATEG list stating that if students learned to analyze "look at" as a prepositional phrase, they "would have to relearn it" as a phrasal verb. The reasoning behind his statement appeared to be simply that he said so. Until someone gives me a better reason, I will accept either explanation.
     "To look," or, if you prefer, "to look at" is an infinitive that functions as an adverb (of purpose) to "drove."

snuffed {at it} and then lowered her nose (DO), and looked {at me}. |

     "Out" here means "outward" and can therefore be considered an adverb; alternatively, "held out" here means "extended" so I would accept either of these explanations. As a prepositional phrase, "out my hand" here does not make sense -- the sentence means "I held my hand out."
     Although I have labeled "near" as an adverb, I would also accept "near to the fence" as a prepositional phrase.
     For "looked at," see the explanation for # 5.
     "Drawing" is a gerundive to "mare."

[DO of "realized" we should get along]] | and then I turned around slowly

and drove away, leaving her gazing {after me}. |

      Since there is nothing that answers the question "along what?," "along" does not usually present my students with a prepositional phrase problem. I have been surprised, however, by the number of my students who, faced with "get along," label "along" as the direct object of "get." I then have to ask them what an "along" is that one can get one. Note that "should get along" here appears to be idiomatic for "should continue on our way." (I cannot tell for certain without the context of the sentence.)
     As with "along," there is nothing that meaningfully functions as the object of "around." Here too, however, some of my students would thoughtlessly label "around slowly" as a prepositional phrase. Again, the only thing we as teachers can do is to stress the importance of Meaning! Meaning! Meaning!
     "Leaving" is a gerundive that modifies "I"; "her" is the direct object of "leaving." Most traditional grammarians would consider "gazing" to be a gerundive to "her." (They would, however, call it a "participle.") In KISS Level Five, students have the option of explaining "her gazing" as a noun absolute that functions as the direct object of "leaving."

     "Out" can be considered part of the verb (which in this case is an infinitive), since "come out" here means "shine." Alternately, if the sun won't come out, that means that it is {in the clouds}. Thus "out" could also be explained as part of an ellipsed prepositional phrase -- "to come out of the clouds."