Scatto una foto dell'albero in giardino.

Scatto is the conjugated verb form. It is the 1st person singular present tense of scattare.

• scattare = to take / to snap
• scatto = I take / I snap

So the sentence starts with a full verb, not the dictionary form.

Italian often drops the subject pronoun because the verb ending already shows who is doing the action.

• scatto already means I take / I snap
• io scatto is possible, but it adds emphasis, contrast, or clarity

So Scatto una foto... is completely normal Italian.

Because foto is feminine in Italian. It is short for fotografia, which is feminine.

So:

• una foto = a photo
• la foto = the photo

Even though the word ends in -o, it is still feminine.

Dell' is a contraction of di + l'.

• di = of
• l'albero = the tree
• di + l'albero → dell'albero

So dell'albero means of the tree.

Because albero begins with a vowel, and the masculine singular definite article becomes l':

• l'albero = the tree

When di combines with l', you get:

• di + l'albero → dell'albero

The apostrophe comes from the article l' before a vowel.

The article is already included inside dell'albero.

So:

• dell'albero = of the tree
• not di l'albero in normal Italian, because Italian contracts them

In other words, the has not disappeared; it is just built into dell'.

In Italian, foto di... is the normal way to say what a photo is of.

Examples:

• una foto del cane = a photo of the dog
• una foto della casa = a photo of the house
• una foto dell'albero = a photo of the tree

This is very similar to English photo of...

Both can be correct, but they feel slightly different.

• in giardino = a very natural everyday way to say in the garden / out in the garden
• nel giardino = more specifically in the garden, with stronger focus on a particular, defined garden

In many everyday situations, Italians very naturally say in giardino without the article.

Most naturally here, it describes the tree:

• Scatto una foto dell'albero in giardino
  = I take a photo of the tree in the garden

That said, without more context, there is a little potential ambiguity, because in giardino could also be understood as the place where the speaker is taking the photo.

If you want to make it clearer:

• Scatto una foto dell'albero che è in giardino = the tree is in the garden
• In giardino, scatto una foto dell'albero = I am in the garden when I take the photo

Yes. The Italian present tense often covers both meanings, depending on context.

So Scatto una foto dell'albero in giardino can mean:

• I take a photo of the tree in the garden
• I am taking a photo of the tree in the garden

If you want to strongly emphasize that the action is happening right now, Italian can also use:

• Sto scattando una foto dell'albero in giardino

Yes. Fare una foto is very common and natural.

So both are possible:

• Scatto una foto = I take / snap a photo
• Faccio una foto = I take a photo

Scattare can sound a little more like to snap, while fare una foto is a very common everyday choice.