Learn Hardcore Japanese: haha ha ribingu no kabe ni kazoku no syasin wo kazarimasu. - My mother decorates the living room wall with family photos.

So 母は… is understood as “As for (my) mother, …” even though 私の is not said. If you were clearly talking about someone else’s mother, you would phrase it differently, often with お母さん plus that person’s name or context.

Why is は used after 母 instead of が?

は marks the topic of the sentence: what you’re talking about.
Here, 母は means “as for my mother,” or “my mother (on the other hand / in this context)”.

You could say 母がリビングの壁に家族の写真を飾ります, but:

母は… = neutral, introducing “mother” as the topic (common, natural).
母が… = focuses more on who does the action, e.g. contrasting with someone else (“It’s my mother who decorates the wall, not me”).

In beginner texts, Xは … is the standard pattern to introduce the main “actor” of a sentence.

What does リビングの壁 literally mean? Is の just “of”?

Literally, リビングの壁 is “the living room’s wall” or “the wall of the living room.”
Here の links two nouns, with the first modifying the second:

リビング = living room
壁 = wall
リビングの壁 = the wall that belongs to / is part of the living room

So it’s similar to “X of Y” or a possessive, but more generally “Noun A’s Noun B” / “Noun B of Noun A.”

Why is the particle に used after 壁? Could we use で here?

With verbs like 飾る (“to display / decorate [something]”), the place where something ends up / is attached usually takes に:

壁にポスターを貼る = put posters on the wall
棚に本を並べる = arrange books on the shelf
壁に家族の写真を飾ります = display family photos on the wall

に here marks the target location for the photos.
で usually marks the place where an action happens (study at school, eat at a restaurant, etc.). With 飾る, using で would sound odd or change the nuance; 壁に…飾る is the natural pattern.

What does 家族の写真 mean exactly? Is it “family’s photos” or “photos of the family”?

In everyday interpretation, 家族の写真 most often means “photos of (my) family” (the family is what appears in the photo).
Grammatically, 家族の is just “family + の” modifying 写真, so it can be understood as:

photos of the family, or
the family’s photos

Context usually makes it clear. In a sentence about decorating a wall, listeners will naturally think of photos showing the family being displayed.

Why does 写真 take を? Isn’t the wall what is being decorated?

In Japanese, with 飾る, the thing you display as decoration takes を:

花を飾る = decorate (a place) with flowers / display flowers
人形を飾る = display dolls
家族の写真を飾る = display family photos (as decoration)

So grammatically, 家族の写真 is the direct object: it’s what you are “placing/displaying.”
The wall (壁) is marked by に as the place where those photos are put. The Japanese sentence is closer to “My mother displays family photos on the living room wall” than “My mother decorates the wall” in a purely structural sense.

What tense is 飾ります? Does it mean “decorate,” “decorates,” or “will decorate”?

飾ります is the polite non‑past form. Non‑past in Japanese covers:

habitual / general actions: “(She) decorates / usually decorates.”
future actions: “(She) will decorate.”

Which English tense you choose depends on context. If it’s describing a routine, you’d translate it as “My mother decorates / puts up family photos…”; if it’s about a future plan, “will decorate / is going to decorate.”

What politeness level is 飾ります? When would I use it?

飾ります is the polite ます‑form of 飾る.
You use the ます‑form when:

Talking to people you are not very close to
Speaking in most public, formal, or neutral situations
Writing in textbooks, news, explanations, etc.

Plain form: 飾る (casual)
Polite form: 飾ります (polite, but not overly formal).
With family or close friends you might say 母がリビングの壁に家族の写真を飾る, but in a textbook or polite conversation, 飾ります is standard.

Can I change the word order, like 母は家族の写真をリビングの壁に飾ります?

Yes. In Japanese, the order of phrases marked by particles is relatively flexible, as long as the verb stays at the end. All of these are grammatical:

母はリビングの壁に家族の写真を飾ります。
母は家族の写真をリビングの壁に飾ります。

The nuance is very similar; sometimes the speaker puts the more “important” or “new” information right before the verb. But both are natural, and the particles (に, を) show the roles clearly.

Could I say お母さん instead of 母 in this sentence?

You can say お母さん here grammatically, but the nuance changes:

母は… = how you usually refer to your own mother when talking to outsiders or in writing. It sounds more neutral and a bit “objective.”
お母さんは… = how you address your mother, or how you might talk about her within the family (e.g. a child saying it).

In a textbook-style sentence describing your family to someone else, 母は… is more appropriate. お母さんは… would sound more like a child talking about “Mom.”

How would I say “There are family photos on the living room wall” (focusing on the state, not on my mother putting them up)?

To describe just the state (photos are there), you typically don’t mention your mother at all. Common patterns:

リビングの壁に家族の写真が飾ってあります。
= “Family photos are (already) displayed on the living room wall.”

Or more simply:

リビングの壁に家族の写真があります。
= “There are family photos on the living room wall.” (Just existence, not specifically “decorated.”)

The original sentence with 母は…飾ります emphasizes who puts them there and the action of decorating.

Is リビング a Japanese word? Why not use リビングルーム or 居間?

リビング is a loanword from English (“living room”), shortened from リビングルーム. All of these are possible:

リビング – very common in modern Japanese, casual / neutral
リビングルーム – longer form, also correct, a bit more formal or descriptive
居間（いま） – native Japanese word, sometimes feels a bit more traditional

In everyday conversation and housing ads, リビング is extremely common, so リビングの壁 sounds very natural.