Vi er uenige om tidspunktet, men enige om planen.

Because the subject is vi (we), which is plural.

In Danish, adjectives used after være (to be) still agree with the subject:

• jeg er enig = I agree
• han er enig = he agrees
• det er enigt = it is agreed / in agreement
• vi er enige = we agree

So in this sentence, both adjectives take the plural form:

• uenige
• enige

The basic forms are:

• enig = agreeing
• uenig = disagreeing

With a plural subject, they become:

• enige
• uenige

Because Danish often leaves out repeated words when the meaning is still clear.

So:

• Vi er uenige om tidspunktet, men enige om planen.

is a shortened version of:

• Vi er uenige om tidspunktet, men er enige om planen.

Both are correct. The shorter version is very natural.

You can think of the second part as having an understood (vi er):

• Vi er uenige om tidspunktet, men (vi er) enige om planen.

Because enig and uenig commonly take om when you say what topic people agree or disagree about.

So:

• enig om noget = agree about something
• uenig om noget = disagree about something

Examples:

• Vi er enige om planen. = We agree about the plan.
• De er uenige om prisen. = They disagree about the price.

A very useful pattern is:

• enig med nogen om noget = agree with someone about something
• uenig med nogen om noget = disagree with someone about something

For example:

• Jeg er enig med dig om ideen. = I agree with you about the idea.
• Jeg er uenig med hende om tidspunktet. = I disagree with her about the time.

So in your sentence, om introduces the subject matter of the agreement/disagreement.

Because Danish usually adds the definite article to the end of the noun.

So:

• et tidspunkt = a time / a point in time
• tidspunktet = the time / the point in time

And:

• en plan = a plan
• planen = the plan

This is very common in Danish:

• en bil → bilen
• et hus → huset
• en idé → idéen/ideen

The endings depend on the noun’s gender:

• en-word often gets -en
• et-word often gets -et

So here:

• tidspunkt is an et-word → tidspunktet
• plan is an en-word → planen

Tidspunktet means the time, but more specifically the point in time or the scheduled time.

It is often used when talking about:

• a specific moment
• an appointment time
• when something should happen

So in this sentence, tidspunktet is not just general time in an abstract sense. It means something more like:

• the timing
• the exact time
• the scheduled time

That is why it fits well with a sentence about disagreement:

• Vi er uenige om tidspunktet = We disagree about the time / the timing

Because Danish often avoids repeating the subject when it is the same in both parts.

So:

• Vi er uenige om tidspunktet, men enige om planen.

naturally means:

• Vi er uenige om tidspunktet, men vi er enige om planen.

The repeated vi is simply left out because it is understood from the first part.

This kind of shortening is very common in Danish, especially when two descriptions are joined with men (but) or og (and).

Yes, in this sentence men means but.

It connects two contrasting ideas:

• disagreement about the time
• agreement about the plan

So the structure is:

• Vi er uenige om tidspunktet = We disagree about the time
• men enige om planen = but agree about the plan

It shows contrast very neatly.

Also, the comma before men is normal in Danish writing.

They are adjectives.

In this sentence they are used with the verb er (are), so the structure is:

• Vi er uenige
• Vi er enige

Literally, this is:

• We are disagreeing/in disagreement
• We are agreeing/in agreement

Danish often expresses this idea with være + adjective, where English may sometimes prefer a verb:

• They agree
• We disagree

But in Danish, at være enig and at være uenig are the standard ways to say this.

Not with vi.

Because vi is plural, you need the plural adjective form:

• vi er enige
• vi er uenige

Using enig or uenig without -e would sound wrong with vi.

Compare:

• Jeg er enig. = I agree.
• Han er uenig. = He disagrees.
• Vi er enige. = We agree.
• De er uenige. = They disagree.

It sounds natural.

It is a very normal Danish way to express:

• agreement on one point
• disagreement on another

The sentence is also nicely compact because Danish often avoids repeating what is obvious:

• no repeated vi
• no repeated er

That makes it sound quite fluent and idiomatic:

• Vi er uenige om tidspunktet, men enige om planen.

Yes, very easily. This is a useful sentence pattern:

• Vi er uenige om X, men enige om Y.

Examples:

• Vi er uenige om prisen, men enige om kvaliteten.
• Vi er uenige om detaljerne, men enige om målet.
• Vi er uenige om datoen, men enige om ideen.

This is a great pattern to memorize because it is common, natural, and flexible.