Wir tauen das Brot erst morgen auf; heute frieren wir den Rest lieber ein.

Because they are separable verbs.

• auftauen → Wir tauen ... auf
• einfrieren → Wir frieren ... ein

In a normal main clause, the conjugated verb goes in second position, and the separable prefix goes to the end of the clause.

So:

• Wir tauen das Brot morgen auf.
• Heute frieren wir den Rest ein.

But when the verb is in the infinitive, the parts stay together:

• Wir wollen das Brot morgen auftauen.
• Wir möchten den Rest einfrieren.

This is the standard verb-second rule in German.

In a German main clause, the finite verb must be in second position. The first position can be taken by different elements, not just the subject.

So if you start with heute, the verb must come next:

• Heute frieren wir den Rest ein.

Structure:

• Heute = position 1
• frieren = position 2
• wir = comes after the verb

This is often called inversion from an English learner’s point of view.

Compare:

• Wir frieren heute den Rest ein.
• Heute frieren wir den Rest ein.

Both are correct; the second one emphasizes today more.

They are the direct objects of the verbs, so they are in the accusative case.

• das Brot is neuter singular, and das is the same in nominative and accusative.
• der Rest is masculine singular, so in the accusative it changes to den Rest.

So:

• das Brot = accusative of das Brot
• den Rest = accusative of der Rest

This happens because:

• etwas auftauen = to thaw something
• etwas einfrieren = to freeze something

Here, erst morgen means not until tomorrow or only tomorrow.

So Wir tauen das Brot erst morgen auf means the action will wait until tomorrow.

This use of erst is very common with time expressions:

• Ich komme erst am Abend. = I’m not coming until the evening.
• Er ist erst 16. = He’s only 16.

So in this sentence, erst adds the idea of delay or not before.

German often uses the present tense to talk about the future, especially when there is a clear time word like morgen.

So:

• Wir tauen das Brot erst morgen auf
  naturally means
• We’ll thaw the bread tomorrow / We’re not thawing the bread until tomorrow

German does have a future form with werden, but it is often unnecessary here:

• Wir werden das Brot erst morgen auftauen.

That is grammatical, but the simple present is more common in everyday speech when the time is already clear.

Lieber means rather or preferably.

In this sentence:

• heute frieren wir den Rest lieber ein

it means something like:

• today we’d rather freeze the rest

So the speaker is expressing a preference: instead of thawing the bread today, freezing the rest today seems like the better option.

A few related forms:

• gern = gladly / like to
• lieber = rather / prefer
• am liebsten = most of all / preferably most

Example:

• Ich trinke lieber Tee. = I’d rather drink tea.

Because ein is the separable prefix of einfrieren, and in a main clause that prefix goes to the end of the clause.

So the clause is built like this:

• Heute
• frieren
• wir
• den Rest
• lieber
• ein

The adverb lieber sits in the middle of the clause, while the prefix ein must wait until the end.

This is normal with separable verbs:

• Ich kaufe heute lieber ein.
• Wir räumen das später auf.

Because the semicolon separates two main clauses, and each main clause normally needs its own subject.

The sentence is really:

• Wir tauen das Brot erst morgen auf;
• heute frieren wir den Rest lieber ein.

Even though the subject is the same in both parts, German normally states it again in a new main clause.

This makes the structure clear and natural.

The semicolon links two closely related independent clauses.

It is stronger than a comma and weaker than a full stop.

So the writer is showing:

• these are two complete clauses
• they are closely connected in meaning

You could also write this as two sentences:

• Wir tauen das Brot erst morgen auf. Heute frieren wir den Rest lieber ein.

Or with a conjunction:

• Wir tauen das Brot erst morgen auf, aber heute frieren wir den Rest lieber ein.

The semicolon is a stylistic way to connect the two ideas neatly.

Yes. Auftauen can be both transitive and intransitive.

In this sentence it is transitive:

• Wir tauen das Brot auf.
  = We thaw the bread.

But it can also be intransitive:

• Das Brot taut auf.
  = The bread is thawing / thaws out.

So German can express either:

• someone thaws something or
• something thaws

The same kind of thing often happens in English too.