Answer:
1. The idea of alien life (proposed many years ago) has not yet been proven- Participle phrase.
The participle phrase starts either with the present (dependably ending with -ing) or past (dependably ending with -ed)
The participle phrase includes the modifiers or objects to complete the thought of the sentence.
2. (According to the letter) the wedding is June 25th.- Prepositional.
A prepositional phrase refers to the phrase which begins with a preposition and ends with the 'objects' of the prepositions that are nouns, gerund, clause or pronoun.
The pattern of the prepositional phrase follows by the object of the preposition having one or more modifiers.
3. Mikayla's homeroom teacher, (mr. Jones) is very proud of her- Appositive
Appositive refers to a word or a noun that is followed by another phrase or noun which identifies or rename the noun or word. In other words, it refers to the literary device which appears after or before a noun phrase or noun, used with a comma.
4. (Talking) is not allowed in class- Gerund
Gerund in a sentence functions as a noun. Hence in a sentence, a gerund will act as direct objects, subjects, subject complements, an object of prepositions or indirect objects. Every gerund ends in -ing, and so does present participles. On the other hand, present participles act as modifiers or complete progressive verbs.
Explanation:
I stood in the back of the crowd, watching as the elf king walked towards the pulpit where the human queen already stood in all the grandness of the twelve regions. She stood, her head held high, her long white hair from years of war flowing freely in the gentle breeze. Her dress was made of golden silk with details of white flowers patterned onto the fabric. She represented the best the human kind had to offer, a willingness to bow and say that this centuries long war would be put to an end.
The elf king dipped his head in return, he was wearing long royal blue robes, his short brown hair pushed back as he straightened again. Setting his quill in the ink first he signed his name followed shortly by our queen.
They shook hands and the crowd cheered. The war was over.
Hope this isn't too long, and hope you like my writing. Just whipped this up. ^-^