Ich weise die Preisgarantie schriftlich nach.

Because the verb is nachweisen, which is a separable verb.

In a normal main clause, separable verbs split into:

• the conjugated stem in second position: weise
• the prefix at the end: nach

So:

• ich weise ... nach

This is very common in German:

• Ich rufe dich an.
• Er kauft ein.
• Wir weisen es nach.

But in an infinitive or with a modal verb, it stays together:

• Ich will die Preisgarantie schriftlich nachweisen.
• Es ist wichtig, die Preisgarantie nachzuweisen.

For the same reason: nachweisen is separable in this sentence.

The full infinitive is nachweisen.
When you conjugate it in a main clause, you split it:

• ich weise ... nach
• du weist ... nach
• er/sie weist ... nach

So weise is just the conjugated verb form for ich.

Compare:

• infinitive: nachweisen
• main clause: Ich weise es nach.

It is accusative, because it is the direct object of the verb nachweisen.

The sentence structure is basically:

• Ich = subject
• weise ... nach = verb
• die Preisgarantie = thing being demonstrated/proven/documented

Since Preisgarantie is a feminine noun, the feminine nominative and accusative article are both die. So the form does not change here:

• nominative: die Preisgarantie
• accusative: die Preisgarantie

That is why you do not see a visible article change.

It is a compound noun, which is extremely common in German.

It is made from:

• Preis = price
• Garantie = guarantee

Together: Preisgarantie

The grammatical gender comes from the last part of the compound, which is Garantie, and Garantie is feminine. So:

• die Garantie
• die Preisgarantie

This rule helps with many German compounds.

Here, schriftlich functions as an adverb, meaning something like in writing or in written form.

It describes how the proof/documentation is provided:

• Ich weise die Preisgarantie schriftlich nach.
  = I provide written proof / I document it in writing.

Even though schriftlich can also be an adjective in other contexts, here it is not modifying a noun directly. It is modifying the action.

Compare:

• ein schriftlicher Nachweis = a written proof/documentation
• Ich weise es schriftlich nach. = I prove/document it in writing

Yes, German word order is somewhat flexible, but the key rule stays the same: in a main clause, the conjugated verb is in second position, and the separable prefix nach stays at the end.

Possible variations include:

• Ich weise die Preisgarantie schriftlich nach.
• Ich weise schriftlich die Preisgarantie nach.
• Die Preisgarantie weise ich schriftlich nach.
• Schriftlich weise ich die Preisgarantie nach.

These all sound slightly different in emphasis.

The version you were given is very natural because it keeps:

• the object together: die Preisgarantie
• the manner adverb after it: schriftlich

Yes. Ich weise ... nach is present tense.

In German, present tense can be used for:

• something happening now
• a general statement
• sometimes even a future action if the context is clear

So this form is grammatically present tense, just as in:

• Ich mache das.
• Ich erkläre es.
• Ich weise es nach.

If you wanted the perfect tense, it would be:

• Ich habe die Preisgarantie schriftlich nachgewiesen.

The past participle is nachgewiesen.

Because nachweisen is a separable verb, the participle usually has:

• prefix + ge
  • verb stem pattern

So:

• nachweisen → nachgewiesen

Examples:

• Ich habe es nachgewiesen.
• Die Preisgarantie wurde schriftlich nachgewiesen.

This is a useful pattern to learn for many separable verbs.

They are related, but not always identical.

• beweisen usually means to prove
• nachweisen often means to prove by evidence, demonstrate, document, verify

In many contexts, nachweisen sounds more like showing evidence or documentation, while beweisen can sound broader or stronger.

For example:

• Er bewies seine Unschuld. = He proved his innocence.
• Sie wies ihre Identität nach. = She proved/verified her identity with evidence.
• Man muss die Zahlung nachweisen. = You have to provide proof of payment.

So in your sentence, nachweisen fits well because it suggests documented or written proof.

Not in this exact structure.

In your sentence, schriftlich is an adverb modifying the verb phrase. If you want it to modify a noun directly, it has to be inflected like an adjective:

• ein schriftlicher Nachweis
• die schriftliche Bestätigung
• eine schriftliche Preisgarantie

So compare:

• Ich weise die Preisgarantie schriftlich nach.
  Here schriftlich describes the action.

• Ich habe einen schriftlichen Nachweis.
  Here schriftlichen describes the noun Nachweis.

It is grammatical and understandable, but it sounds somewhat formal or business-like.

That is because:

• Preisgarantie is a formal compound noun
• nachweisen is a formal verb often used in official, legal, technical, or customer-service contexts
• schriftlich also adds a formal tone

So this sounds like something you might see in:

• customer service
• contracts
• business communication
• official correspondence

In casual speech, people might choose simpler wording depending on the context.