Wir halten an diesem Plan fest.

Because festhalten is a separable verb in German.

The full verb is festhalten, but in a normal main clause, the prefix fest separates and moves to the end:

• Wir halten ... fest.

This is very common with separable verbs:

• Ich rufe dich an. → from anrufen
• Er steht früh auf. → from aufstehen
• Wir halten an diesem Plan fest. → from an etwas festhalten

In some other structures, the verb stays together:

• Wir wollen an diesem Plan festhalten.
• dass wir an diesem Plan festhalten

So fest is at the end because the verb is being used in a main clause.

Not exactly. In this sentence, an etwas festhalten is an idiomatic expression.

It often means:

• to stick to something
• to maintain something
• to keep to something
• to insist on something

So in Wir halten an diesem Plan fest, the meaning is not literally physically holding a plan in your hands. It means keeping the plan and not changing it.

German often uses verbs in both literal and idiomatic ways, and festhalten is a good example:

• literal: Er hält das Seil fest. = He is holding the rope tightly.
• idiomatic: Wir halten an diesem Plan fest. = We are sticking to this plan.

Because the expression is an etwas festhalten.

The verb phrase requires the preposition an, so the thing you are sticking to comes after an:

• an diesem Plan
• an der Entscheidung
• an seiner Meinung

You cannot normally say Wir halten diesen Plan fest with the same meaning. That would sound like a different structure and would not express sticking to a plan.

So it is important to learn this as a whole pattern:

• an + something + festhalten

Because an here takes the dative case.

In an diesem Plan:

• an = preposition
• diesem = dative form of dieser
• Plan = masculine noun

For a masculine noun in the dative, dieser becomes diesem:

• nominative: dieser Plan
• accusative: diesen Plan
• dative: diesem Plan

So:

• Wir halten an diesem Plan fest.

uses dative because an etwas festhalten takes an + dative.

No. An is a two-way preposition (Wechselpräposition), which means it can take either:

• accusative for direction/movement toward something
• dative for location or certain fixed verb-preposition combinations

Examples:

• Ich hänge das Bild an die Wand.
  accusative, because there is movement toward the wall

• Das Bild hängt an der Wand.
  dative, because it describes location

But in an etwas festhalten, the verb expression is fixed and normally uses dative:

• an diesem Plan
• an der Idee
• an alten Regeln

So in your sentence, the dative is not about physical location. It is just the case required by the expression.

The base form is:

• an etwas festhalten

This is how you would usually write it in a dictionary or vocabulary list.

Its principal parts are:

• infinitive: festhalten
• present: er hält fest
• past: hielt fest
• past participle: festgehalten

With the preposition included:

• an etwas festhalten
• an etwas festgehalten haben

This is useful because many German verbs are best learned together with their preposition and case.

Because in a German main clause, the conjugated verb must come in the second position.

Here, the conjugated verb is halten:

• Wir = subject
• halten = conjugated verb in second position
• an diesem Plan = prepositional phrase
• fest = separated prefix at the end

So the sentence structure is:

• Wir | halten | an diesem Plan | fest.

German word order often works like this with separable verbs:

1. subject or another element first
2. conjugated verb second
3. other sentence elements
4. separable prefix at the end

Usually no, not if you mean we are sticking to this plan.

To express that meaning, you need:

• Wir halten an diesem Plan fest.

Without an, the sentence changes and may sound wrong or suggest a different meaning. The idiomatic construction is specifically:

• an + dative + festhalten

So for this meaning, it is best to treat an etwas festhalten as one unit.

Yes, it is in the present tense:

• Wir halten ... fest.

But like English, German present tense can often express a current stance that continues into the future.

So this sentence can mean:

• we are sticking to this plan now
• we intend to continue with this plan

German often uses the present tense where English might also use will or going to, depending on context.

Yes. Depending on context, German speakers might also say:

• Wir bleiben bei diesem Plan.
• Wir halten an dem Plan fest.
• Wir verfolgen diesen Plan weiter.
• Wir weichen nicht von diesem Plan ab.

But there are slight differences:

• an etwas festhalten emphasizes sticking to something
• bei etwas bleiben is often a little more conversational: to stay with something
• nicht von etwas abweichen sounds more formal: not deviate from something

So Wir halten an diesem Plan fest is a very natural and standard way to express firm commitment to a plan.

Yes, both are possible.

• an diesem Plan = to this plan / this particular plan
• an dem Plan = to the plan

The difference is just the determiner:

• diesem points to this plan specifically
• dem refers to the plan

So both are grammatically correct:

• Wir halten an diesem Plan fest.
• Wir halten an dem Plan fest.

The original sentence simply uses this plan rather than the plan.

It is most common with things such as:

• Pläne
• Ideen
• Prinzipien
• Regeln
• Entscheidungen
• Meinungen

For example:

• Sie hält an ihrer Meinung fest.
• Wir halten an unseren Prinzipien fest.

With people, it is much less common in this exact idiomatic sense. Usually it is used for positions, decisions, beliefs, or commitments rather than people themselves.

So in everyday German, an etwas festhalten is mainly about sticking to an idea, decision, rule, or plan.