There are two things to know about Islamic beliefs that could help you understand which of these answers is correct.
First, you need to know that Muslims consider figurative art to be idolatrous. Figurative art, as opposed to abstract art, is art that is meant to look like something from the real world. Many Muslims take very seriously the Biblical injunction against creating graven images. This is not explicitly stated in the Koran, but the Koran is very strongly against idolatry. So, Muslims generally are much less likely than people from other religions to make art that actually depicts human or other life-like figures.
Second, you need to know that the language of the Koran is particularly sacred to Muslims. Muslims believe that the words of the Koran were given, in Arabic, to Muhammad by God. Therefore, the Arabic words of the Koran are extremely important to many Muslims.
Given these facts, you should be able to see that calligraphy is the thing that is a significant feature of Islamic art. Life-sized statues and pictures of Muhammad would clearly violate the ban on images of people or things. Hieroglyphics of the Egyptian sort might do this as well. By contrast, calligraphy is acceptable and Arabic calligraphy (particularly from the Koran) is seen as something sacred and therefore a good subject for artistic expression.
Islamic Art has origins dating back to the Roman and Byzantine Empires. It makes heavy use of blue and gold colors.
I am currently learning the Arabic language and the writing over in the Middle East is very unique. It is very similar to English cursive. Most of the letters in the alphabet connect (accept for 5 letters). Because of the unique writing style, Arabs often use it in art.
Often times on the outside tile of mosques are white, blue and gold (sometimes even brown) colored collages. These designs often consist of star shapes (Jordan sometimes has 7 pointed stars hence the 7 point star its the flag).
As for portraits of Muhammad, I can't say I've seen many. I'm sure at one point they might've been influential to the art, but now, not so much.
I wouldn't say that hieroglyphics played a big part in forming the art style there either, but you never know. With all my time spent over there, I don't believe I've ever seen any hieroglyphics.
I've only seen life-sized statues in the capital city. They mainly put them in the 'duwars' (circles). ([The roads in the Middle East are different, and instead of having many intersections, they have circles (they also have traffic lights, but only in minor intersections). This is a place where there is a strip of pavement forming a circular shape and a bunch of different roads connect to the circle. When a person wants to turn onto a different road, they turn right and drive around the circle until they have reached their turnoff point.]) Anyway, in the middle of these 'duwar's is a circular patch of pavement (sometimes grass), but for decoration, statues are placed in the middle of these circle. Sometimes these statues contain that star-shape pattern, other-times, they are statues of abstract art.
Personally, I believe that the calligraphic writing has had the biggest impact on Islamic art. Because of its daily use and its unique style, many Arabs have taken pride in it and portrayed it in their artwork.