Sagittarius the Archer, is right behind Scorpius the Scorpion. both visible in the summer sky - south if you live in the Northern Hemisphere.
Beta Sagittarii (Arkab) is located in the posterior leg of Sagittarius.
A star chart
The answer will depend on where on earth you are trying to view it from.
Sagittarius should appear highest in the sky at midnight right around the First of the Year, and it doesn't matter where on Earth you are.
Epsilon Sagittarius (Kaus Australis) is the southern portion of the bow.
In the constellation of Sagittarius.
The constellation Sagittarius represents a centaur with a bow. Its name, in Latin, means archer. Sagittarius is one of the constellations listed by Ptolemy in the second century.
On (well, mostly south of) the ecliptic between Sagittarius and Libra.
The galactic center is in the general direction of Sagittarius. Is that what you were asking?
NGC 6723 is a globular cluster in the constellation Sagittarius.
We can only speculate, and different people may have different opinions. To understand the true motive, you would have to inquire of He who placed those stars in those particular places in the sky. Or else consult the ancient individuals who looked at that group of stars, decided what it looked like to them, and gave it the name Sagittarius.