Ik werk op kantoor.

Because ik takes the singular verb form werk.

The infinitive is werken = to work.
When you conjugate it in the present tense:

• ik werk = I work
• jij werkt = you work
• hij/zij werkt = he/she works
• wij werken = we work
• jullie werken = you work
• zij werken = they work

So after ik, you normally use the verb without -en.

This is one of those expressions where Dutch uses a different preposition from English.

In English, you often say in an office or at the office.
In Dutch, the usual idiomatic phrase is op kantoor.

So:

• Ik werk op kantoor = I work in an office / at the office

Dutch often uses op for places connected with work, school, or institutions:

• op school = at school
• op kantoor = at the office / in an office
• op het werk = at work

Using in kantoor would sound unnatural in normal Dutch.

Because op kantoor is a fixed expression.

In Dutch, some place expressions often appear without an article when you mean the general function of the place, not one specific building or room.

So:

• op kantoor = at the office / in an office, in a general sense
• op het kantoor = at the office, but now referring to a specific office

Compare the difference:

• Ik werk op kantoor.
  General statement: my job is office-based.

• Ik werk op het kantoor van mijn vader.
  Specific office: my father’s office.

It usually means that your work takes place in an office environment.

Depending on context, English might translate it as:

• I work in an office.
• I work at the office.
• sometimes even I do office work, depending on context

So it does not always point to one exact office building. Often it simply contrasts office work with other kinds of work, like:

• Ik werk op kantoor, niet thuis. = I work at the office, not at home.
• Ik werk op kantoor, niet in een winkel. = I work in an office, not in a shop.

It is a het word:

• het kantoor = the office

That is useful when you want to make it definite or add adjectives:

• het grote kantoor = the big office
• op het kantoor = at the office / in the office

But in the sentence Ik werk op kantoor, the article is simply omitted because of the fixed expression.

Yes, but they mean something slightly different.

• Ik werk op kantoor.
  The most natural general sentence. It means your job is office-based or you work at the office.

• Ik werk in een kantoor.
  This emphasizes the physical type of place: in an office. It is grammatical, but less idiomatic as a neutral everyday statement.

• Ik werk op het kantoor.
  This usually refers to a specific office already known from context.

So if you are just learning the basic everyday way to say it, Ik werk op kantoor is the best choice.

The word order is the normal Dutch main-clause order:

subject + finite verb + rest

So here:

• Ik = subject
• werk = finite verb
• op kantoor = prepositional phrase

This is very similar to basic English word order:

• I work at the office.

Dutch word order changes more in other clause types, but in a simple main sentence like this, it is straightforward.

A rough English-friendly guide would be:

ik verk op kan-TOOR

A few notes:

• ik: the i is short, a bit like the vowel in bit
• werk: the w sounds more like an English v
• kantoor: stress is on the second syllable: kan-TOOR

More approximately:

• Ik → like ick
• werk → close to verk
• op → like op
• kantoor → kan-TOOR

The r may sound different from English depending on the speaker’s accent.

Yes. Dutch op kantoor is broader than either single English version.

Depending on context, it can mean:

• you work at the office rather than at home
• you work in an office rather than outdoors, in a shop, in a factory, etc.
• your job is office-based

So English chooses between at the office and in an office, but Dutch often just uses op kantoor for all of these.

You can do it like this:

Negative:

• Ik werk niet op kantoor. = I do not work at the office / in an office.

Question:

• Werk je op kantoor? = Do you work at the office / in an office?

Notice that in a yes/no question, the verb comes first:

• Werk = verb
• je = subject
• op kantoor = rest

That verb-first pattern is very common in Dutch questions.