Quiero el que está sobre la mesa.

Here el que means the one that or the one which.

So Quiero el que está sobre la mesa literally works like:

I want the one that is on the table.

Spanish often uses el / la / los / las + que to avoid repeating a noun that is already understood from the context.

Because que here is introducing a description of an omitted noun.

In English, we say the one that is on the table.
In Spanish, that the one part is often expressed as el que.

For example, if you are choosing between several books, pens, or phones, Spanish can leave the noun unstated:

• Quiero el que está sobre la mesa. = I want the one on the table.

The noun is understood from context.

No noun is written, but one is understood.

For example, it could mean:

• Quiero el libro que está sobre la mesa.
• Quiero el vaso que está sobre la mesa.
• Quiero el móvil que está sobre la mesa.

Instead of repeating the noun, Spanish uses el que if the noun is masculine singular.

The form changes with gender and number:

• el que = masculine singular
• la que = feminine singular
• los que = masculine plural
• las que = feminine plural

Because the sentence is talking about location, and location in Spanish is normally expressed with estar, not ser.

So:

• está sobre la mesa = is on the table

Using es here would be wrong for normal location.

A very useful rule is:

• ser = identity, characteristics, origin, etc.
• estar = location, condition, temporary states

It means on the table or more literally over/on top of the table.

In many situations, sobre can mean on.
However, in everyday spoken Spanish, especially in Spain, encima de la mesa is often more common and more natural for physical position.

So all of these may appear, depending on context:

• sobre la mesa
• encima de la mesa
• sometimes en la mesa in certain contexts, though that can sound more like on the table surface / at the table, depending on meaning

In this sentence, sobre la mesa is correct and clear.

It is correct and understandable in Spain, but in everyday conversation many speakers would more often say encima de la mesa for a physical object resting on the table.

So these are both possible:

• Quiero el que está sobre la mesa.
• Quiero el que está encima de la mesa.

The second can sound a bit more colloquial and concrete in everyday speech.

Sometimes yes, but the meaning is not exactly the same.

• el que está sobre la mesa = the one that is on the table
• el de la mesa = the one from the table / the one belonging to the table / the one associated with the table, depending on context

So el de la mesa is more ambiguous. It does not clearly mean the one that is on the table unless the context makes that obvious.

If you specifically want to identify something by its position, el que está sobre la mesa is clearer.

Because el que refers to a specific understood noun, while lo que usually refers to what, that which, or an abstract idea.

Compare:

• Quiero el que está sobre la mesa. = I want the one that is on the table.
• Quiero lo que está sobre la mesa. = I want what is on the table.

The second version is broader and less specific. It can mean I want whatever is on the table.

So el que points to one specific item of a known type, while lo que does not.

The accent is required because está is a conjugated verb form of estar.

• está = he/she/it is, you are, or it is
• esta without an accent is a demonstrative word, as in esta mesa = this table

So the accent helps distinguish the verb from the demonstrative form.

It can refer to a person, but the context has to make that clear.

For example:

• Quiero al que está sobre la mesa would not normally make sense, because a person is not usually on a table.
• But in another context, el que lleva gafas could mean the one who is wearing glasses.

In your sentence, because of sobre la mesa, it almost certainly refers to an object.

Also notice: when referring to a person as a direct object, Spanish may use the personal a:

• Quiero al que está allí. = I want the one who is there.

Not very naturally.

A word-for-word version would be something like:

I want the one that is on the table.

That is understandable, but in natural English we often shorten it to:

• I want the one on the table.

Spanish is doing something very normal with el que, even though English often sounds slightly simpler.

You would change the article and the relative phrase to match the omitted noun.

Examples:

• Quiero la que está sobre la mesa. = I want the one on the table.
  Used if the missing noun is feminine singular.

• Quiero los que están sobre la mesa. = I want the ones on the table.
  Used if the missing noun is masculine plural.

• Quiero las que están sobre la mesa. = I want the ones on the table.
  Used if the missing noun is feminine plural.

Notice that the verb also changes in the plural:

• está → están

Yes. Quiero el que está sobre la mesa is the normal, natural order.

It follows a common Spanish pattern:

• verb + object
• then a relative clause describing that object

So:

• Quiero = I want
• el que = the one that
• está sobre la mesa = is on the table

Other word orders are possible in special contexts, but this version is the straightforward standard one.