Learn Hardcore Spanish (Latin America): Creo en la justicia e igualdad en mi familia. - I believe in justice and equality in my family.

Since igualdad starts with the sound /i/, you say justicia e igualdad, not justicia y igualdad.
This is just to make pronunciation smoother; the meaning is still “and.”

Why do we say creo en instead of just creo la justicia or creo la justicia e igualdad?

The verb creer normally needs a preposition when you “believe in” something as a value or concept, and that preposition is en:

Creo en Dios. – I believe in God.
Creo en la justicia. – I believe in justice.

Creo la justicia would sound wrong/odd in Spanish. To say “I believe that… + sentence,” you use creer que:

Creo que la justicia es importante. – I believe that justice is important.

Why is there la before justicia e igualdad? Why not just Creo en justicia e igualdad?

In Spanish, abstract nouns like justicia, igualdad, libertad often take the definite article la when we talk about them in a general, “in principle” way:

Creo en la justicia.
Luchamos por la igualdad.

Here, la applies to both feminine nouns: la justicia e igualdad (“justice and equality”).
You can say Creo en justicia e igualdad, but it sounds more slogan-like or poetic; the version with la is more standard in everyday speech.

Could I say la justicia y la igualdad instead of la justicia e igualdad?

Yes. You could say:

Creo en la justicia y la igualdad en mi familia.

Differences:

e igualdad is used because of the sound /i/ in igualdad.
Repeating the article (la justicia y la igualdad) slightly emphasizes each noun separately.
Both are grammatically correct and natural.

Why is it mi familia and not mis familia, since a family has many people?

In Spanish, the possessive mi/mis agrees with the grammatical number of the noun, not with how many people it refers to in real life.

familia is a singular noun → mi familia (my family)
familias would be plural → mis familias (my families)

So you must say en mi familia.

What exactly does en mi familia mean here? “In my family,” “for my family,” or something else?

Literally en mi familia means “in my family” or “within my family.”
The idea is usually: Within the context of my family, I believe in justice and equality (as values that guide how family members treat each other).

If you wanted to stress “for my family” (as a benefit or goal), you could say para mi familia.
If you wanted “with my family,” you would say con mi familia.

Does en mi familia modify creo or justicia e igualdad? Is the meaning ambiguous?

Grammatically, en mi familia can be read either way:

Creo en la justicia e igualdad, en mi familia.
→ I believe in justice and equality in the context of my family.
Creo en la justicia e igualdad en mi familia.
→ I believe in justice and equality within my family (how things work inside the family).

In practice, both readings are very close and people will normally understand it as “These are values I believe in for how my family should be.”
If you wanted to make the “context” clearer, you could say:
En mi familia, creo en la justicia e igualdad.

Why is there no yo? Could I say Yo creo en la justicia e igualdad en mi familia?

Spanish usually drops subject pronouns because the verb ending already shows the subject:

creo → clearly “I believe”
crees → “you believe”
cree → “he/she believes”

So Creo en la justicia… is completely normal and natural.
You can add yo (Yo creo en la justicia…) for emphasis or contrast, like:
Yo creo en la justicia, pero otros no.

What verb tense is creo, and does it mean “I think” or “I believe” here?

Creo is the present indicative, first person singular of creer.

Creer can mean either:

“to believe” (about faith, values, principles):
Creo en la justicia.
“to think” / “I guess” (giving an opinion about facts):
Creo que llegará tarde. – I think he’ll arrive late.

In your sentence, with creer en + noun, it clearly means “I believe in justice and equality.”

Is this sentence natural in Latin American Spanish, or does it sound more like Spain?

The sentence Creo en la justicia e igualdad en mi familia is completely natural and neutral; it works in Latin America and in Spain.

There is no region-specific vocabulary or grammar here.
If anything, in everyday speech many people in Latin America might spontaneously say y igualdad instead of e igualdad, but e igualdad is the formally correct version.

Why aren’t justicia and igualdad capitalized, like English sometimes capitalizes “Justice” or “Equality” in slogans?

In Spanish, common nouns are not capitalized in normal sentences, even when they refer to big values or ideals:

La justicia es importante.
Luchamos por la paz y la igualdad.

They only get capital letters if they’re part of a proper name (for example, the name of an organization, a party, a holiday, etc.).
So justicia and igualdad are correctly written in lowercase here.

Could I move en mi familia to the beginning and say: En mi familia, creo en la justicia e igualdad? Is that okay?

Yes, that’s perfectly correct and very natural:

En mi familia, creo en la justicia e igualdad.

Putting en mi familia at the start emphasizes the context (your family) a bit more.
The overall meaning is the same; Spanish word order is flexible for these kinds of adverbial phrases.