Der Backofen ist heiß, also lege ich das Schneidebrett lieber weiter weg.

No. In this sentence, also means so, therefore, or thus.

• Der Backofen ist heiß, also ... = The oven is hot, so ...

If you want to say English also in German, the usual word is auch.

Because the sentence contains two main clauses:

• Der Backofen ist heiß
• also lege ich das Schneidebrett lieber weiter weg

German normally separates clauses like this with a comma. Here also links the second clause to the first one.

German main clauses usually follow the verb-second rule.

That means the conjugated verb must come in the second position:

• Ich lege das Schneidebrett weg.
• Also lege ich das Schneidebrett weg.

Here, also takes the first position, so lege must come next, and ich comes after that.

Here lieber means rather, preferably, or in natural English I’d better.

It shows preference and often makes the statement sound a bit softer or more cautious.

• Ich gehe lieber zu Fuß. = I’d rather walk.
• Ich lege das Schneidebrett lieber weiter weg. = I’d better put the cutting board farther away.

You can think of this as the separable verb weglegen, meaning to put away or move aside.

In a main clause, the prefix weg- separates and moves to the end:

• Ich lege das Schneidebrett weg.

In your sentence, weiter is added to show that it is being moved farther away:

• Ich lege das Schneidebrett weiter weg.

Weiter is the comparative of weit, so it means farther or further.

• weg = away
• weiter weg = farther away

It does not necessarily mean a great distance. It just means not so close.

The object of legen is in the accusative case, because you are putting something somewhere.

But das stays das in both nominative and accusative singular:

• nominative: das Schneidebrett
• accusative: das Schneidebrett

So the case is changing grammatically, but the form looks the same.

You can see the change more clearly with a masculine noun:

• der Tisch → den Tisch

German often uses different verbs depending on how an object is positioned:

• legen = to lay something down, usually flat
• stellen = to stand something up, usually upright

A cutting board is normally thought of as something you lay down, so legen is the natural choice.

German nouns have grammatical gender, and compound nouns take the gender of the last element.

• der Backofen because der Ofen is masculine
• das Schneidebrett because das Brett is neuter

So the last part of the compound tells you the gender.

It is a compound noun:

• Schneide- from schneiden = to cut
• Brett = board

So Schneidebrett literally means cutting board.

This is very common in German: several words are combined into one longer noun.

Yes.

• Backofen specifically means a kitchen oven
• Ofen is more general and can mean a stove, heater, or oven depending on context

So Backofen is the more precise word here.

Yes, but the structure changes:

• Der Backofen ist heiß, also lege ich das Schneidebrett lieber weiter weg.
• Ich lege das Schneidebrett lieber weiter weg, weil der Backofen heiß ist.

With weil, the verb goes to the end of the subordinate clause:

• weil der Backofen heiß ist