Learn Hardcore Spanish (Latin America): Yo mantengo el contacto con mi familia por teléfono.

Yo mantengo... and Mantengo... both mean I keep...
You would normally use Yo only for emphasis or contrast, e.g. Yo mantengo el contacto, pero mi hermano no.

Why is the verb mantengo and not something like mantieno?

The infinitive is mantener, and it is irregular in the yo form of the present tense:

yo mantengo
tú mantienes
él/ella/usted mantiene
nosotros mantenemos
vosotros mantenéis
ellos/ustedes mantienen

So the irregularity is only in mantengo; the other forms have -ie- (mantienes, mantiene, etc.), but yo uses -engo.

What exactly does mantener el contacto mean compared to just contactar or hablar?

Mantener el contacto literally means to maintain contact, and it suggests an ongoing, regular relationship, like to keep in touch.

contactar is more like to contact (someone) at a particular moment.
hablar is simply to talk.

So:

Mantengo el contacto con mi familia = I keep in touch with my family (regularly).
Contacto a mi familia = I contact my family (I get in touch with them, maybe once or in a specific situation).
Hablo con mi familia = I talk with my family (focus on the act of talking, not the idea of maintaining contact over time).

Why is it mantengo el contacto and not mantengo contacto?

Both are possible, but they have slightly different feels:

Mantengo el contacto (with the article) is the standard, idiomatic expression for I keep in touch.
Mantengo contacto (without el) sounds a bit more general or abstract, like I maintain (some) contact, and is less common in everyday speech.

In practice, natives almost always say mantener el contacto.

What’s the difference between mantengo el contacto and me mantengo en contacto?

Both mean I keep in touch, but the structure changes:

Mantengo el contacto con mi familia:
- Verb + direct object (el contacto).
- Slightly more neutral/literal.
Me mantengo en contacto con mi familia:
- Reflexive verb (me mantengo) + expression en contacto.
- Feels a bit more idiomatic or conversational to many speakers.

Meaning-wise, they’re practically the same; you can use either. Another very common variant is Estoy en contacto con mi familia.

Why is it con mi familia and not a mi familia or de mi familia?

Because the verb mantener (el) contacto typically uses con to indicate with whom you have the contact:

mantener el contacto con alguien = to keep in touch with someone

Using the others would be wrong here:

a mi familia would suggest direction (e.g. llamar a mi familia = to call my family).
de mi familia would convey of/from my family (possession or origin), not with my family.

So con is the natural preposition in this expression.

Why is it mi familia and not mis familia?

In Spanish, familia is grammatically singular (la familia), even though it refers to multiple people.

Possessive adjectives agree with the grammatical number of the noun, not with how many people it represents:

mi familia = my family (one family, singular noun)
mis padres = my parents (plural noun)
mis hermanos = my siblings/brothers (plural noun)

So you must say mi familia, not mis familia.

Why do we use por teléfono instead of en el teléfono or al teléfono?

Por here expresses the means or medium through which something happens:

por teléfono = by phone / over the phone
por correo = by mail
por WhatsApp = by WhatsApp

Other options mean different things:

en el teléfono usually means physically on the phone (device or call):
- Estoy en el teléfono could mean I’m on the phone (talking) or on the telephone (physically), depending on context.
al teléfono is used mainly with verbs like llamar:
- Llamo a mi madre al teléfono de casa = I call my mother on the home phone.

For expressing the communication channel, por teléfono is the standard choice.

Could I say this in a different order, like Yo mantengo el contacto por teléfono con mi familia?

Yes. Spanish word order is flexible. All of these are correct:

Yo mantengo el contacto con mi familia por teléfono.
Yo mantengo el contacto por teléfono con mi familia.
Mantengo el contacto con mi familia por teléfono.

The most natural everyday version is probably Mantengo el contacto con mi familia por teléfono, but the others are fine and mean the same. Word order changes emphasis slightly, but not the basic meaning.

What’s the difference between teléfono, teléfono móvil, and celular?

Teléfono by itself just means phone; context usually tells you if it’s mobile or landline.

For mobile phones:

In most of Latin America, celular (or teléfono celular) is the common term.
In Spain, móvil or teléfono móvil is used.

So in Latin America, you might also hear:

Mantengo el contacto con mi familia por celular.
Hablo con mi familia por WhatsApp.

Is mantengo el contacto con mi familia por teléfono formal, or can I use it in everyday speech?

It’s neutral and perfectly fine in everyday speech.

If you want even more casual options, you could say:

Hablo con mi familia por teléfono. = I talk to my family on the phone.
Me comunico con mi familia por teléfono. = I communicate with my family by phone.
Estoy en contacto con mi familia por teléfono. = I’m in touch with my family by phone.

But your original sentence sounds natural and common.

Why is the simple present used (mantengo) instead of something like estoy manteniendo?

In Spanish, the simple present is the default way to express habitual actions and general facts:

Mantengo el contacto con mi familia por teléfono.
= I keep in touch / I maintain contact (as a regular habit).

The present progressive (estoy manteniendo) is used mainly when the action is happening right now or in a very limited time frame, and with mantener el contacto that sounds odd in most contexts.

So for routines, always prefer the simple present: mantengo, hablo, llamo, etc.