Mi madre me enseña la foto del viaje.

Me is the indirect object pronoun. It tells you to whom the photo is being shown.

So in Mi madre me enseña la foto del viaje:

• mi madre = the subject, the person doing the action
• me = the person receiving the action, to me
• enseña = shows
• la foto del viaje = the thing being shown

A very literal breakdown would be: My mother shows me the photo of the trip.

Enseña is the third-person singular present form of enseñar.

The verb must agree with mi madre, which is she:

• yo enseño
• tú enseñas
• él / ella enseña

Since mi madre = she, you use enseña.

Yes — enseñar can mean both to teach and to show, depending on context.

In this sentence, because the object is la foto, the natural meaning is to show.

Common patterns:

• enseñar algo a alguien = to show something to someone
• enseñar algo / enseñar a alguien in other contexts can mean to teach

So here, me enseña la foto means she shows me the photo, not she teaches me the photo.

La foto means the photo, so it refers to a specific photo that both speaker and listener can identify from context.

If you said una foto, it would mean a photo, which sounds less specific.

So the article changes the meaning:

• la foto = the photo, a particular one
• una foto = a photo, any one / one among others

Because de + el contracts to del in Spanish.

So:

• de el viaje → del viaje

This contraction is required in normal Spanish.

A useful rule:

• a + el = al
• de + el = del

But note that this does not happen with la:

• de la foto stays de la foto

It means the photo of the trip or the trip photo, depending on how natural you want the English to sound.

The structure is:

• la foto = the photo
• del viaje = of the trip / from the trip

In everyday English, you might translate it as:

• the photo from the trip
• the photo of the trip

The Spanish phrase is very normal and simply links the photo to the trip.

Because me is already an indirect object pronoun.

When Spanish uses a full noun instead of a pronoun, you often see a:

• Mi madre le enseña la foto a Juan.

Here:

• le = to him
• a Juan = clarifies who le refers to

But with just me, you do not add another a:

• Mi madre me enseña la foto.

So me already contains the idea of to me.

No. Me cannot go there in normal Spanish.

Object pronouns like me, te, le, nos usually go:

1. before a conjugated verb
   • Mi madre me enseña la foto del viaje.

or

2. attached to an infinitive, gerund, or affirmative command
   • va a enseñarme
   • está enseñándome
   • enséñame

Since enseña here is a normal conjugated verb, me must go before it.

Yes. Mostrar is also a very common verb for to show.

So both are possible:

• Mi madre me enseña la foto del viaje
• Mi madre me muestra la foto del viaje

In this kind of sentence, both sound natural.
Very broadly:

• mostrar is a straightforward show
• enseñar can also mean show, and is extremely common in everyday Spanish

In a neutral sentence like this, mi madre is the normal choice, because Spanish usually uses a possessive to specify whose mother you mean.

So:

• mi madre = my mother

Just madre by itself would usually need a special context, for example in poetry, older-style language, or certain fixed expressions.

So for a learner, the safe normal form is mi madre.

The present tense in Spanish can do both, just like in English.

So Mi madre me enseña la foto del viaje could mean:

• My mother is showing me the photo of the trip (right now, depending on context)
• My mother shows me the photo of the trip (habitual or simple present meaning)

Context tells you which one is intended.

If you wanted to emphasize right now, Spanish could also say:

• Mi madre me está enseñando la foto del viaje.

Yes, but the original order is the most neutral and natural.

Normal order:

• Mi madre me enseña la foto del viaje.

You can also move things around for emphasis, especially in speech:

• La foto del viaje me la enseña mi madre.
• Me enseña la foto del viaje mi madre.
  This is possible, but it sounds marked and less neutral.

Because Spanish is more flexible with word order than English, changing the order often changes the focus or emphasis, not the basic meaning.

Because la foto del viaje already identifies the photo well enough in context. Spanish often prefers a simple noun phrase with the definite article when the meaning is clear.

If you said su foto del viaje, that would mean his/her/their photo from the trip, and it introduces the question of whose photo it is.

So:

• la foto del viaje = the photo from the trip
• su foto del viaje = his/her/their photo from the trip

The original sentence does not need that extra information.