Komoda za koju smo pričvrstili dasku stoji pored zida.

Because the verb pattern is pričvrstiti nešto za nešto = to attach something to something. The preposition za is part of that construction, so it must stay when the second thing is replaced by a relative pronoun.

So:

• pričvrstili smo dasku za komodu = we attached the board to the dresser
• komoda za koju smo pričvrstili dasku = the dresser to which we attached the board

Without za, the sentence would be ungrammatical here.

Because the relative pronoun must match the noun komoda in gender and number, but its case depends on its role inside the relative clause.

Here:

• komoda is feminine singular
• the pronoun comes after za
• za here takes the accusative

So the correct form is koju.

A quick comparison:

• koja = nominative feminine singular
• koju = accusative feminine singular

Because dasku is the accusative singular of daska. It is the direct object of pričvrstili.

Base form:

• daska = board / plank

In the sentence:

• pričvrstili dasku = attached the board

Smo is a clitic auxiliary, and Serbian clitics usually go in the second position of their clause.

In the relative clause, the first unit is za koju, so the clitic smo comes right after it:

• za koju smo pričvrstili dasku

You may also hear other word orders in Serbian, but this one is very standard and natural.

Pričvrstili means attached, fastened, or fixed. It is the past participle form used with smo to make the past tense.

The verb is pričvrstiti, which is perfective. That means it presents the action as completed: the board was successfully attached.

In Serbian, stojati often means to stand in the sense of to be standing / to be positioned somewhere. With furniture, this is very natural.

So:

• Komoda stoji pored zida = The dresser stands next to the wall
• more naturally in English: The dresser is next to the wall

Serbian often uses a more physical verb where English might just use is.

Because pored requires the genitive case. The noun zid therefore changes to zida.

So:

• zid = wall
• pored zida = next to / beside the wall

This is a very common pattern:

• pored kuće = next to the house
• pored stola = next to the table

It can be translated literally that way, but it sounds awkward in English. A more natural English version would be:

• The dresser that we attached the board to is next to the wall.
• The dresser to which we attached the board is next to the wall.

So the Serbian is normal, but English usually prefers a slightly different structure.

Yes, Serbian word order is fairly flexible, especially for emphasis or style. For example:

• Komoda za koju smo pričvrstili dasku stoji pored zida.
• Pored zida stoji komoda za koju smo pričvrstili dasku.

Both are grammatical. The original version is neutral, while starting with pored zida puts more focus on the location.

Because Serbian uses the relative pronoun koju to refer back to komoda, just as English uses which, that, or whom-type structures in relative clauses.

So instead of repeating komoda, Serbian says:

• komoda za koju... = the dresser to which...

This is the normal way to connect the main noun with extra information about it.