You may want to get a copy of Gods, Demons and Symbols of Ancient Mesopotamia An Illustrated Dictionary by Jeremy Black and Anthony Green.
They give excellent information and pictures of the material you are looking at.
As you know the Babylonians used a sexagesimal system of counting, multiples of 60 and in particular the number 3600 (60 squared) for which they had a special word (sar), and on occasion 36000. Numbers were sometimes used to write the names of the most important deities. Some numbers acquire special religious or magical significance for essentially mathematical reasons.
The wrist band actually has 11 points. 7 and 11 are two important numbers in Ancient Mesopotamia. The wrist band represents the 11 'Slain Heroes'. The Slain Heroes may ultimately have contributed to Greek myths of Near Eastern origin, such as the Labours of Herakles. Also Tiamat gives birth to 11 monsters, or groups of monsters (bearing some resemblance to the Slain Heroes defeated by Ningirsu or Ninurtu in a story of earlier origin).
Under the number 7 we have the Seven Demons, Seven Dots (later to become 8), Seven Gods and Seven Sages.
These are not to be taken literally as they are symbolism and allegory. You will see Pleiades and Zodiacal connections, creation stories etc. There is too much material to key in.
The picture you posted is of a ritual being performed. Academics have been arguing this ritual and the objects in it for a very long time. They believe it to be a "purification" ritual, I have a different take on it.
I don't want to get into all of the symbolism encrypted into these scenes but I will give you a list of the various interpretations.
Here is the academic point of view.
"This ceremony or 'ritual' is called the 'cone-smearing'. The ritual includes a magically protective rite, a benediction, an anointing of a symbol of the king, or of the king himself (the cones sometime also being held behind the king's head), a literal rendering of fruit-picking or of the fertilization of the date palm, of the god Dumuzi, a symbolic reference to fire and water as the elements of life, or a piece of astronomical symbolism.
The Genies who hold the cone and bucket are sometimes hybrids such as the griffin-demon appear to take part in rituals, but more often such participants are anthropomorphic. Some types are clearly minor deities, since they wear the horned cap as a mark of divinity; others may be human. A male winged god, standing or kneeling, holds a bucket and cone and can be involved in the scenes of 'ritual' centred on the stylized tree."
The cone represents the sun or male principle and the bucket with water represents the moon or female principle. There is a tree usually found in these motifs. In Mesopotamian art the 'stylized' or 'sacred' tree, or, more presumptuously, as the 'tree of life', has provoked more discussion and controversy than almost any other element in it. As with the equally ubiquitous and often iconographically associated 'winged disc', opinions vary greatly as to the meaning and significance of the symbol, and lack of explicit textual reference to the tree or its function allows speculation a free rein.
Stylized trees of one type or another are commonly portrayed in Mesopotamian art from prehistoric times through to the Neo-Babylonian Period.
What I believe is being represented in this Mesopotamian motif is the 'sacred marriage' or Hieros Gamos in todays more modern ritual language.