Mr Mudakuma Lukallimka's reply:

I passed on this question to a friend of mine, who is both a qualified astronomer and an experienced student of cuneiform, Dr. Mathieu OSSENDRIJVER.

Today I got his response, which reads:

"Concerning possible alignment of ziqqurats:

It appears that, unlike Egyptian pyramids, mesopotamian temples and ziqqurats(temple towers) were not systematically aligned to any direction. This is what a brief look at a random sample of maps of temple complexes suggests to me.
However, I'm not aware of any systematic study of this phenomenon in Mesopotamia for all periods, so I am not able to make a definite statement.

Concerning the 'star of Ishtar':

Ishtar is the name of an important Babylonian goddess associated with love and war. Her astral representative is the planet Venus, which is therefore sometimes simply called Ishtar, among other names, such as Dilbat, Inanna or Ninsianna. The cuneiform signs which are used to write
Ishtar consist of the determinative MUL, which signifies that the word is the name of a star or a planet, plus the name of the deity. Thus, very likely, the element MUL is not to be
translated, as was sometimes done in old translations ('star of Ishtar').

It is commonly believed that the deity Ishtar is of semitic (i.e. akkadian) origin, but in Babylonia the semitic Ishtar was equated with the sumerian goddess Inanna, who had similar functions, already at a very early date in the third millennium. Thus it is difficult to identify which characteristics of Ishtar were adopted from Inanna and which ones may be attributed to the heritage of the Akkadians.

From a comparison of Akkadian and Sumerian texts mentioning Ishtar or Inanna,it appears that 1)Inanna has always been a female deity, and 2) that she was originally identified mainly with Venus as an evening star. Both aspects are frequently attested in sumerian religious texts from southern Mesopotamia (Uruk, Nippur). The deity Ishtar however appears to have been a male deity originally, as is shown by texts from places in Syria and northern Mesopotamia such as Ebla, which are thought to have been less influenced by Sumerian culture. He was associated mainly with Venus as a morning star. As such, Ishtar was sometimes depicted wearing a beard, even as late as under the reign of the Assyrian king Assurbanipal.
This should not be seen as evidence that the Assyrian or Babylonian Ishtar was of two sexes. Rather, the Babylonians and Assyrians had come to consider Ishtar as being a female very early already, through the merging with the Sumerian Inanna.

Furthermore, there is no evidence for the presence of a male Ishtar in any Babylonian or Assyrian temple: all the Ishtar deities in temples appear to have been female. But one aspect of the original Ishtar was not completely forgotten, namely
that in its astronomical function as the morning star, Ishtar is in fact male. It must be pointed out, though, that the Babylonians and Assyrians were themselves rather confused by this, so that they would sometimes call Venus as an evening star the male Ishtar, and Venus as a morning star the female Ishtar.

Venus/Ishtar played an important role in babylonian astrology, and five tablets of the astrological omen series, Enuma Anu Enlil, (from about 1100 BC onwards) are devoted to Venus. In fact, out of the planetary omens the Venus omens form the largest group, even exceeding Jupiter (2 tablets). In these omens, Venus is referred to as Ninsianna, Dilbat or Ishtar.

Concerning the importance of astronomy and astrology for the Babylonians:

This is a complex question that would require a long answer since one must distinguish between different periods, and because many aspects are unclear. Certainly the stars played a very important role for all ancient Mesopotamian peoples throughout all periods, much more so than for the Egyptians. Thus already the Sumerians (2500-2000 BC) believed that many of their main gods had astral representations, such as Utu (the Sun), Nanna (the Moon), Inanna (Venus). There is no evidence however that the Sumerians had any sophisticated astronomical knowledge about the motion of the planets, although they may have been aware of schematic periods for the appearance and disappearance of Venus for instance.
Also, we do not have astrological omina written by the Sumerians.

It seems that the emergence of the semitic Akkadians brought with it an increased interest in astrology. Thus from the Old Babylonian time onwards (1850 BC) we have astrological
omens written in Akkadian (Babylonian), often precursors of what later (1100 BC) becomes the big omen series Enuma Anu Enlil. This series remained widely copied and used until the very end of the ancient Mesopotamian civilisation. It shows that at least in this period, the study of celestial phenomena were an important method of gaining information about the will and action of the gods. As such it stands besides other methods such as studying the liver of sheep, although the application of omen astrology seems to have been somewhat restricted to the king and his palace as compared to liver omens.

Only very late, from the Persian time onwards (450 BC) do we find horoscopic astrology in Mesopotamia, which is rather like the later Greek and western types of astrology that are still used today. The goal of these horoscopes was to predict the future of newborns based on the position of the planets at birth.

Astronomy as a natural science developed also rather late (from about 800 BC onwards) but separately from astrology.
Originally its motivation was probably partly astrological and calendaric.

A full mathematical theory which is able to accurately predict the motion of the planets and of the Moon exists finally in the Seleucid and Parthian periods (300 BC-100 AD). The dominant theme of these theories is the calculation of the time and position of the new moon, which signalled the beginning of a new month. However, similar mathematical theories were succesfully applied to the planets. The motivation for constructing these theories is not really known - it may have been simple scientific curiosity, since they appear to have no astrological use."