ميزان التسوية على الرف.

Because this is a nominal sentence in Arabic. In the present tense, Arabic usually does not use a separate word for is / are.

So:

• ميزان التسوية على الرف
  literally: The leveling tool / level on the shelf
• natural English: The leveling tool is on the shelf

Arabic simply puts the topic first and then the information about it after that.

It is a nominal sentence made of:

• ميزان التسوية = the subject/topic
• على الرف = the predicate/comment

More specifically:

• ميزان التسوية is a noun phrase
• على الرف is a prepositional phrase meaning on the shelf

So the structure is:

• [noun phrase] + [prepositional phrase]

This is a very common pattern in Arabic for expressing location.

Yes. ميزان التسوية is an iḍāfa (genitive/possessive construction).

That means it is built as:

• ميزان = scale / balance / level
• التسوية = leveling / adjustment / equalization

Together, the phrase literally means something like:

• the scale/instrument of leveling
• or more naturally, a compound noun such as leveling instrument or spirit level, depending on context

In an iḍāfa:

1. The first noun does not take ال
2. The second noun is in the genitive
3. The whole phrase can be definite if the second noun is definite

Because in an iḍāfa, the first noun normally does not take ال.

So Arabic says:

• ميزان التسوية

not:

• الميزان التسوية

The definiteness comes from the second noun, التسوية, which has ال. That makes the whole phrase definite.

So ميزان التسوية means the leveling instrument / the spirit level, not just a leveling instrument.

Because it is the second part of the iḍāfa, and it carries the definiteness of the whole expression.

Compare the idea:

• كتاب طالب = a student’s book or book of a student → not fully definite
• كتاب الطالب = the student’s book → definite

Likewise:

• ميزان تسوية could sound more indefinite or generic
• ميزان التسوية is definite

So ال on التسوية helps make the whole noun phrase definite.

Because على means on or on top of, while في means in or inside.

A shelf is usually treated as a surface, so Arabic naturally says:

• على الرف = on the shelf

If you said في الرف, that would suggest something more like inside the shelf/cabinet, which is a different idea.

In careful full MSA, it would be:

ميزانُ التسويةِ على الرفِّ

Here is why:

• ميزانُ → nominative, because it is the subject/topic of the nominal sentence
• التسويةِ → genitive, because it is the second term of the iḍāfa
• الرفِّ → genitive, because it comes after the preposition على

Also note:

• ميزان does not take tanwīn here, because it is the first term of an iḍāfa

A careful pronunciation is roughly:

mīzānu t-taswiyati ʿalā r-raffi

In pause, many speakers would say something closer to:

mīzān at-taswiya ʿalā r-raff

A few pronunciation notes:

• In التسوية, the ل of ال is assimilated because ت is a sun letter, so it sounds like at-taswiya
• In الرف, the ل is also assimilated because ر is a sun letter, so it sounds like ar-raff

So the written ال is there, but the l sound is not pronounced in those two words.

Yes, but the meaning or emphasis may shift.

The basic order here is natural and neutral:

• ميزان التسوية على الرف = The leveling instrument is on the shelf

But Arabic can also front the prepositional phrase for emphasis:

• على الرف ميزان التسوية

That gives more focus to the location, something like:

• On the shelf is the leveling instrument
• or It is on the shelf that the leveling instrument is

So the original version is the most straightforward, neutral order.

التسوية comes from a root related to making something even, level, adjusted, or equal.

Depending on context, it can mean things like:

• leveling
• adjustment
• equalization
• settlement

In this sentence, because it is part of ميزان التسوية, the context suggests a tool or instrument connected with leveling.

So the exact English translation may vary by context, but grammatically it is still the same structure.

Yes, but that would be a slightly different structure.

• ميزان التسوية = an iḍāfa construction, often tighter and more noun-like, like a compound term
• ميزان للتسوية = a scale/instrument for leveling, using لـ to express purpose

So:

• ميزان التسوية sounds more like a fixed noun phrase or technical term
• ميزان للتسوية sounds more descriptive: an instrument for leveling

Both can be understandable, but ميزان التسوية is more compact and more typical for this kind of compound expression.