Hi ha una foto penjada a la paret sobre el sofà.

It means there is.

In Catalan, hi ha is the normal way to say that something exists or is present somewhere.

• Hi ha una foto = There is a photo
• Hi ha dues fotos = There are two photos

A useful thing to remember: hi ha is used for both singular and plural.

Because this sentence is introducing the existence of something.

• Hi ha una foto... = There is a photo...
• La foto està penjada... = The photo is hanging / is hung...
• És una foto antiga. = It is an old photo.

So:

• hi ha = says something exists / is there
• està = says where something already known is, or what state it is in
• és = identifies or describes what something is

Because foto is a feminine noun in Catalan.

It is short for fotografia, which is also feminine, so it keeps the feminine gender:

• una foto
• la foto
• les fotos

This is one of those nouns where the ending -o does not mean masculine.

Because penjada agrees with foto, which is feminine singular.

Here penjada is the past participle of penjar (to hang) used like an adjective, meaning hung or hanging.

Agreement:

• penjat = masculine singular
• penjada = feminine singular
• penjats = masculine plural
• penjades = feminine plural

So:

• una foto penjada
• un quadre penjat
• dues fotos penjades

Catalan often uses a participle or adjective after the noun instead of a full verb phrase.

So una foto penjada a la paret is literally something like:

• a photo hung on the wall
• or more naturally, a photo hanging on the wall

If you want a full verb, you can say:

• La foto està penjada a la paret. = The photo is hanging / is hung on the wall.

In your sentence, penjada is just describing foto.

Yes.

• Hi ha una foto a la paret sobre el sofà.

This still makes sense and means there is a photo on the wall above the sofa.

Adding penjada makes the image more explicit: the photo is hung up on the wall. It sounds very natural, especially because photos and pictures are commonly described this way.

In this kind of expression, a la paret means on the wall.

Catalan often uses a where English uses on, especially with location in certain fixed expressions.

So:

• penjada a la paret = hung on the wall

It is best learned as an idiomatic pattern:

• a la paret
• a la porta
• a la finestra, etc., depending on context

Also:

• paret = wall
• la paret = the wall

Here it means above the sofa or over the sofa.

Because the sentence already says the photo is on the wall, the natural interpretation is:

• the photo is hanging on the wall
• and that position is above the sofa

So it does not mean the photo is resting on top of the sofa.

Also, sobre can have a few meanings in Catalan depending on context, but here above/over is the right one.

In practical meaning, it locates the photo: the photo is on the wall, and that wall position is above the sofa.

English learners sometimes see possible ambiguity here, because the phrase comes after paret. But in normal usage, the sentence is understood as:

• There is a photo hanging on the wall above the sofa.

So the whole location works together:

• a la paret = on the wall
• sobre el sofà = above the sofa

No, Catalan word order is somewhat flexible.

The version you have is natural and neutral:

• Hi ha una foto penjada a la paret sobre el sofà.

But Catalan can move location phrases for emphasis, for example:

• Sobre el sofà hi ha una foto penjada a la paret.
• A la paret sobre el sofà hi ha una foto penjada.

Starting with Hi ha is very common when you are introducing something new into the conversation.