Learn Hardcore Danish: Væggen bag sofaen er dækket af farverige malerier og anden kunst. - The wall behind the sofa is covered with colorful paintings and other art.

You don’t add any article to bag itself. Bag just stays the same and is followed by a noun (often in the definite form when we mean a specific object).

What exactly does er dækket af mean grammatically?

Er dækket af is a stative passive construction:

er = is (present tense of at være, to be)
dækket = covered (past participle of at dække, to cover)
af = by / with

So er dækket af literally means “is covered by/with”, describing a state (the wall is in a covered condition), not an action happening right now.

Compare:

De dækker væggen med malerier. = They cover the wall with paintings. (active)
Væggen er dækket af malerier. = The wall is covered with paintings. (stative, focusing on the result).

Why is it dækket af and not dækket med?

Both dækket af and dækket med exist, but they have slightly different feels:

dækket af often highlights what is doing the covering, and is the more neutral/common choice in many descriptions.
dækket med can feel a bit more like “using X as the covering material”.

In this sentence, er dækket af farverige malerier og anden kunst is fully natural and idiomatic. Saying dækket med here would also be understandable, but af is more typical in this kind of general description of a surface covered by objects.

Why is sofaen also in the definite form?

Sofaen is the definite singular form of en sofa:

en sofa = a sofa
sofaen = the sofa

We are talking about a specific sofa (the one in the room being described), not just any random sofa. So both nouns are definite and specific:

Væggen bag sofaen = the wall behind the sofa

Why does farverige end in -e?

Farverige is an adjective meaning “colourful”, and it takes the plural ending -e because it describes a plural noun:

et maleri = a painting (singular, neuter)
malerier = paintings (plural)
farverige malerier = colourful paintings

In Danish, adjectives normally take -e in the plural, regardless of gender:

et stort maleri → store malerier
et farverigt maleri → farverige malerier

So farverige is plural to match malerier.

What is the difference between malerier and billeder?

Both can be translated as “pictures”, but they are not identical:

et maleri / malerier = a painting / paintings (specifically works made with paint, like oil paintings, acrylic, etc.)
et billede / billeder = a picture / pictures (much broader: photos, drawings, paintings, images on a screen, etc.)

So farverige malerier emphasises that these are paintings as an art form, not just any kind of images.

Why is it malerier og anden kunst and not malerier og andre kunst?

The key point is that kunst is used here as a mass (uncountable) noun, like “art” in English.

anden is the common-gender singular form of “other”.
andre is the plural form.

Since kunst is treated as a singular mass noun (like water, furniture, art in English), you use the singular form:

anden kunst = other art (more art of another kind)

If you were talking about countable pieces of art, you might say something like:

andre kunstværker = other works of art (plural, so andre).

Why is there no article before anden kunst (why not en anden kunst)?

Because kunst here is used as an uncountable/mass noun meaning “art in general”.

In both Danish and English, mass nouns usually don’t take an indefinite article:

English: art, music, furniture (not an art in the general sense)
Danish: kunst, musik, møbler (in a general sense, no en/et)

So:

anden kunst = other art (more art of a different kind)

If you say en anden kunst, it sounds more like “a different kind of art” (a specific type), which is a narrower, more abstract idea. In the sentence given, anden kunst is just “other artworks / other kinds of art” in a general, non-countable sense.

How do the genders and forms of the nouns work in this sentence?

Nouns in the sentence:

væggen
- base form: en væg (common gender)
- definite singular: væggen
sofaen
- base form: en sofa (common gender)
- definite singular: sofaen
malerier
- base form: et maleri (neuter)
- plural indefinite: malerier
kunst
- base form: en kunst (in theory common gender)
- but here used as a mass noun, normally without article in this sense

The determiners and adjective endings then follow from these forms:

Væggen (definite common)
sofaen (definite common)
farverige malerier (plural, so farverige with -e ending)
anden kunst (kunst as a singular mass noun, so anden, not andre).

Is the word order Væggen bag sofaen er dækket af ... normal in Danish?

Yes, it’s the standard main-clause word order:

Subject: Væggen bag sofaen
Verb: er
Predicative / rest of the clause: dækket af farverige malerier og anden kunst

Danish main clauses usually follow Subject–Verb–Object/Complement order, very similar to English here. The prepositional phrase bag sofaen just modifies væggen and stays right after it, before the verb:

Væggen bag sofaen er ... = The wall behind the sofa is ...

How is the whole sentence pronounced, and are there any tricky words?

A fairly neutral pronunciation (simplified IPA) could be:

Væggen bag sofaen er dækket af farverige malerier og anden kunst.
/ˈvɛgən bɑːˀ ˈsoːfɑn ʌ ˈdɛgəd ɑ fɑˈʁeːviə ˌmɑləˈʁiːɐ ɔ ˈanən kʰɔnst/

Things English speakers often find tricky:

Væggen: the æg is like “vegh-”, and the final -gen is weak /-ən/, not a hard g.
bag: often pronounced more like /bɑː/, with a long a, and a very weak or glottal end, not like English bag.
sofaen: stress on so-, and -en is a light -n sound.
og: usually pronounced /ɔ/, almost like short “aw”, not like English og or ogg.
dækket: first syllable dæk- like “deck” but with a more open vowel, second syllable weak -et /-əd/.

Putting it all together with natural rhythm will help the sentence feel much more “Danish” when you say it.