Rambam Yesodei HaTorah 7:3
הדברים שמודיעין לנביא במראה הנבואה--דרך משל מודיעין לו, ומיד ייחקק בליבו פתרון המשל במראה הנבואה, ויידע מה הוא
(My paraphrasing): The prophet is shown a prophetic image, as a type of parable, and immediately realizes the resolution of the parable, and knows what it is.
Ramchal, towards the end of Da'as Tevunos (siman 186-188), explains this further. He explains that the understanding of the prophet went according to his individual makeup, and that all prophets except Moses saw a vision that was not entirely clear.
As to the second questions, in siman 190, he explains why this system was the way prophecy worked.
The first point he says is that Hashem wanted to reveal Himself to mankind according to the nature of mankind, which is that the form which is assumed "below" (in this world) is a representation of the spiritual flow which is its source. So too the prophecy would be presented as a manifestation, with a form, of its source. In this way prophecy parallels the rest of creation, in that the supernal matters are not directly revealed, but are perceived through their relationship to the creations.
The second point he makes is that certainly everything that exists is the way it is in order to reflect some aspect of spiritual reality. Therefore, for example, man was created with eyes in order to reflect Hashem's providence. And everything is exact in that way, and if not that Hashem wanted to reflect some concept in this way, it wouldn't be created this way. Therefore, the prophecy, by using images, is shown to the prophet in order that he understand how this flow is connected from the spiritual to the physical world. (See there at length for greater detail)
The Malbim in Parshas Beha'aloscha, on the words במראה אתודע אליו, explains this with a different approach. He explains that all prophets grasped Hashem through His emanation into this world - they perceived this world as having a reality to it, and they related to Hashem from within the world (as opposed to Moshe, who, to a degree, was able to grasp Hashem as He exists beyond the confines of finite existence). Therefore, when they receive a Divine message, it is through the medium of this world and its tools that they receive the message. Thus the verse describes that "regular" prophets see Hashem במראה (with a komatz), which means a mirror - they can only see the side of the vision that they are standing on. Moshe on the other hand, sees במראה (with a segol), which means a lens - he is able to see through to the other side.
