I had to pick what grammatical stucture is in the "" portion of the sentence.

Choses are
adverb clause
infinitive phrase
past participial
elliptical clause
adjective clause
present participial phrase
nominative absoolute
appossitive
past participle phrase
prepositional phrase with a gerund
1. Put the sizes on the uniforms "while sorting them out". Adjective clause
2. By mistake I opened a package "addressed to my sister". Past participial phrase
3. The hero falls in love with a countness "who is very beautiful". Adverb Clause
4. My most valuable coin, "one from Spain", is worth more than $100.00. Appositive
5. "The weather remaining turbulent", we will postpone our canoe trip. Nominative absolute.
6. "Headed by a senior", the group drew up rules for School Spirit Week. Present Participial phrase
7. "By serving as a popcorn vendor",Don saw many good games. past Part. Phrase
8. We walked along the mountain path "looking for unusuall flowers". Present Part. Phrase.

Did I get these right? thank you for checking for me.

1. incorrect

2. correct

3. incorrect

4. correct

5. probably correct; I'd also call it a dangling modifier!!

6. incorrect

7. incorrect

8. correct

thank you

Your answers are mostly correct!

1. "while sorting them out" is not an adjective clause, but a present participial phrase.
2. "addressed to my sister" is indeed a past participial phrase.
3. "who is very beautiful" is an adjective clause.
4. "one from Spain" is indeed an appositive.
5. "The weather remaining turbulent" is actually a participial phrase, specifically a present participial phrase.
6. "Headed by a senior" is a present participial phrase.
7. "By serving as a popcorn vendor" is a prepositional phrase with a gerund.
8. "looking for unusual flowers" is a present participial phrase.

So, you got 5 out of 8 correct. Great job!