No
No
No, it's a noun. Incidentally, "end of the week" is not a sentence, it is a phrase.
A preposition refers to the position of an object therefore in this sentence "at home" is the prepositional phrase
No, that wouldn't be a complete sentence. You could end a phrase with are. eg You are stupid. No I am not. You are!
Yes, as a matter of fact, a prepositional phrase is usually stated at the end of most sentences.
The noun or pronoun at the end of a prepositional phrase is the object of the preposition.
Yes. There is no word or phrase in English that cannot begin or end a sentence.
Both - A full-stop indicates the end of the current sentence or phrase, and lets the reader know a new sentence or phrase is about to start.
Yes, it is, 'the end' is a sentence just like 'happy birthday', you may always f there are no subject and predicate in that little phrase but it's a sentence!
Where is the sentence? If you mean in the one you just stated, in this sentence is the prepositional phrase.
The mud adhered to his shoes.
The word at the end of a prepositional phrase is called the object of the preposition. It is the noun or pronoun that the preposition acts upon in the sentence.