Yes cannot start a prepositional phrase because it's not a preposition.
yes for example, in the tree, or, in the cage
Yes, in the classroom is a prepositional phrase.
Yes, for counting is a prepositional phrase.
Yes, the phrase from the refrigerator is a prepositional phrase. from is a preposition
Yes. The prepositional phrase is on the ground.
Yes, "in time" is an adverbial prepositional phrase.
Yes, the word "by" is a prepositional phrase. No, the word "by" is a preposition; a prepositional phrase including the word "by" would be "... by the wayside."
Yes, around the tree is a prepositional phrase.
Yes, "over the rainbow" is a prepositional phrase.
I'm not sure if your question is whether a prepositional phrase is the same thing as a word group, or if "group" is a prepositional phrase. The answer is no in either case. A word group must express a complete thought. A prepositional phrase is part of a sentence and it has to start with a preposition. "In the group" is a prepositional phrase beginning with the preposition "in."
Yes, "within" is a preposition in the prepositional phrase "within a prepositional phrase" which functions to show the relationship between "within" and "prepositional phrase".
yes it is