Das Foto ist alt, aber wertvoll.

Because Foto is a neuter noun in German, so it takes the article das.

• das Foto = the photo
• ein Foto = a photo

German nouns have grammatical gender, and you usually have to learn the noun together with its article.

German often uses more phonetic spelling than English. The word is commonly written Foto, with F, because that matches the sound.

You may also see Photographie in some formal or older contexts, but in everyday German:

• das Foto = the photo
• fotografieren = to photograph

So Foto is the normal modern spelling.

In a normal German statement, the finite verb usually comes in position 2. This is one of the most important word-order rules in German.

Here:

• Das Foto = subject
• ist = verb
• alt = adjective/complement
• aber wertvoll = contrast + second adjective

So the pattern is:

Subject + verb + rest

That is why you get Das Foto ist alt ...

Adjectives in German only take endings in certain situations, especially when they come before a noun.

But here, alt and wertvoll come after the verb ist. In that position, they are predicate adjectives, and predicate adjectives do not take endings.

Compare:

• Das Foto ist alt.
  The photo is old.
  → no adjective ending

• das alte Foto
  the old photo
  → adjective ending appears because the adjective is before the noun

The same applies to wertvoll:

• Das Foto ist wertvoll.
• das wertvolle Foto

Aber means but and connects two contrasting ideas.

Here, the contrast is:

• it is old
• but it is also valuable

So aber works very much like English but.

In German, clauses connected by conjunctions like aber are normally separated by a comma.

So:

• Das Foto ist alt, aber wertvoll.

This is standard German punctuation. Even though the second part is short, the comma is still used.

German can omit repeated words when the meaning is clear. The full version could be:

• Das Foto ist alt, aber es ist wertvoll.
• or even Das Foto ist alt, aber ist wertvoll would not be natural

The natural sentence is simply:

• Das Foto ist alt, aber wertvoll.

The second ist is understood from the first part. English does this too sometimes:

• The photo is old, but valuable.

Yes, wertvoll is a common word. It means valuable.

It is made up of:

• Wert = value
• voll = full of

So literally, it is something like full of value. In real use, though, you should just understand it as valuable.

It can describe:

• expensive things
• important objects
• sentimental items
• historically significant things

A simple English-friendly guide is:

• wertvoll ≈ VAIRT-foll

A bit more closely:

• wert sounds somewhat like vairt
• voll sounds like foll

A few details:

• w in German sounds like English v
• v in voll sounds like English f
• the r in standard German is often not strongly pronounced like in English

• Das is capitalized because it is the first word of the sentence.
• Foto is capitalized because all German nouns are capitalized.

This is a major difference from English. In German:

• das Foto
• der Tisch
• die Musik

Nouns are always capitalized, even in the middle of a sentence.

Yes, but Bild and Foto are not always exactly the same.

• das Foto = a photo / photograph
• das Bild = picture / image / painting, depending on context

So if you specifically mean a photograph, Foto is the more precise word.
If you mean a picture more generally, Bild may work.

Sometimes, yes, but the meaning or tone may change.

For example:

• Das Foto ist alt, aber wertvoll. = The photo is old, but valuable.
• Das Foto ist alt und wertvoll. = The photo is old and valuable.
  This just adds both facts, without emphasizing contrast.

So aber is used because being old might sound negative at first, while valuable adds a contrasting positive idea.