qǐng zài qīngdān shàng xiě biānhào.

Here, 请 means please. It makes the sentence polite:

• 请写编号。 = Please write the number/code.
• 请在清单上写编号。 = Please write the number/code on the list.

In other contexts, 请 can also mean to invite or to ask/request, but in this sentence it is just a polite marker at the beginning.

在 introduces the location of the action. It often means at, in, on depending on context.

In this sentence:

• 在清单上 = on the list

So 在 tells you where the writing should happen.

A very common pattern is:

• 在 + place + verb

For example:

• 在纸上写字 = write characters on paper
• 在墙上挂画 = hang a picture on the wall

Chinese often uses a structure like:

• 在 + noun + 上 / 里 / 下

These words such as 上, 里, and 下 are sometimes called location words or localizers.

So:

• 清单上 = on the list
• 桌子上 = on the table
• 书里 = in the book

Even though English just says on the list, Chinese usually needs both parts:

• 在 marks location
• 上 shows the specific spatial relationship: on

So 在清单上 is the natural full expression.

Usually, no. 在清单写编号 sounds incomplete or unnatural.

The normal form is:

• 在清单上写编号

That is because 清单 is the noun, and 上 tells you the action happens on that surface/document.

You can think of 清单上 as one unit meaning on the list.

Chinese usually puts the location before the main verb.

So the structure is:

• 请
  • 在清单上
    • 写
      • 编号

Literally:

• Please + on the list + write + number/code

This is very normal in Chinese. Time, place, and manner often come before the verb.

Compare:

• 我在纸上写名字。 = I write my name on the paper.
• 请在这里等。 = Please wait here.

编号 usually means a number used for identification, such as:

• a serial number
• an item number
• a reference number
• a code number

It is not just any number in the abstract.

For comparison:

• 数字 = digit/number as a mathematical concept
• 号码 = number such as a phone number or room number
• 编号 = an assigned identifying number/code

So in this sentence, 编号 most likely means an identifying number that should be written on the list.

Here, 编号 is a noun: the number/code.

It is the object of 写:

• 写编号 = write the number/code

But in other sentences, 编号 can also be a verb meaning to number or to assign numbers.

For example:

• 这些文件已经编号了。 = These documents have already been numbered.

So yes, 编号 can be either a noun or a verb, but in your sentence it is a noun.

In Chinese, the subject is often omitted when it is obvious from context, especially in commands or instructions.

So:

• 请在清单上写编号。

implicitly means:

• (你)请在清单上写编号。
• Please write the number/code on the list.

Including 你 is possible, but often unnecessary.

Chinese does not have articles like a, an, or the.

So:

• 清单 can mean a list or the list
• 编号 can mean a number/code or the number/code

The exact meaning depends on context.

That is very normal in Chinese, and learners need to get used to nouns appearing without articles.

Yes, a similar sentence could be:

• 请把编号写在清单上。

This also means Please write the number/code on the list.

The difference is mostly in focus:

• 请在清单上写编号。 emphasizes the location first: on the list
• 请把编号写在清单上。 brings the object 编号 forward and then shows what to do with it

Both are natural, but your original sentence is a very straightforward instruction.

Not exactly.

• 清单 = a list, checklist, inventory, itemized list
• 名单 = a list of names

So if the document is a general list or checklist, 清单 is correct. If it is specifically a name list, 名单 may be more appropriate.

Even if the translation is already given, it helps to know the natural sense.

写编号 does not always mean physically writing a random number. It often means:

• write the item number
• fill in the reference number
• enter the code number

So the exact English wording depends on context, but the Chinese structure is simply:

• 写 = write
• 编号 = identifying number/code

It is fairly neutral and polite.

• 请 makes it polite
• the rest is straightforward and practical

It sounds like an instruction you might see:

• on a form
• in an office
• in a warehouse
• in written instructions

It is not especially casual, but not highly formal either.