Quiero convencer a mi amiga de ir al festival de cine conmigo.

This is the personal a, used in Spanish before a specific person who is the direct object of the verb.

In Quiero convencer a mi amiga..., the person being convinced is my friend, so Spanish adds a:

• convencer a alguien = to convince someone

You would not normally translate this a into English. It is just a grammar marker.

Compare:

• Veo a mi amiga. = I see my friend.
• Veo la película. = I see the film.

The first has the personal a because mi amiga is a person.

Because convencer commonly works with this pattern in Spanish:

• convencer a alguien de algo
• convencer a alguien de + infinitive

So:

• Convencí a Juan de la idea. = I convinced Juan about the idea.
• Convencí a Juan de venir. = I convinced Juan to come.

In your sentence:

• convencer a mi amiga de ir al festival...

means to convince my friend to go to the festival...

This is just the normal structure of the verb, and it does not match English word-for-word.

After convencer a alguien de..., Spanish often uses the infinitive when talking about the action someone is being convinced to do.

So:

• convencer a alguien de ir = to convince someone to go
• convencer a alguien de estudiar = to convince someone to study

You do not use de va, because va is a conjugated verb, and after de here Spanish wants an infinitive.

You can also say:

• Quiero convencer a mi amiga para que vaya al festival...

That version uses para que + subjunctive and is also natural. But your original sentence is more compact and very common.

Because a + el contracts to al in Spanish.

So:

• a + el = al

That is why you say:

• ir al festival
• voy al cine
• vamos al centro

The only common exception is when el is part of a proper name:

• Voy a El Escorial.

But in normal cases like el festival, you must use al.

Spanish often uses de where English uses another noun as an adjective.

So:

• festival de cine = film festival
• literally: festival of cinema

This is very common in Spanish:

• tienda de ropa = clothes shop
• mesa de madera = wooden table
• sala de estar = living room

So de cine describes what kind of festival it is.

After con, the pronouns yo and tú have special forms:

• conmigo = with me
• contigo = with you

So you say:

• Ven conmigo. = Come with me.
• Voy contigo. = I’m going with you.

Not:

• con mí
• con tú

These are fixed forms you simply have to learn.

Because it naturally goes with ir al festival:

• ir al festival conmigo = to go to the festival with me

Putting conmigo at the end sounds very natural because it comes after the action phrase it belongs to.

The sentence flows like this:

• Quiero = I want
• convencer a mi amiga = to convince my friend
• de ir al festival de cine conmigo = to go to the film festival with me

You could move things around in some contexts, but the original order is the most neutral and natural.

In standard modern Spanish, possessives like mi, tu, su, nuestro usually replace the article.

So you say:

• mi amiga = my friend
• mi coche = my car
• nuestra casa = our house

Not normally:

• la mi amiga

That sounds old-fashioned or dialectal, not standard everyday Spanish.

No. Mi is the same for both masculine and feminine singular nouns.

So:

• mi amigo = my male friend
• mi amiga = my female friend

For the plural, it becomes mis:

• mis amigos
• mis amigas

So the gender changes in amigo / amiga, not in mi.

Yes, sometimes, but they are not always exactly the same.

• convencer often emphasizes making someone mentally agree or accept something.
• persuadir often emphasizes successfully getting someone to do something.

In everyday use, there is overlap, and both can often work. But convencer is extremely common in sentences like this.

For example:

• Quiero convencer a mi amiga de ir...
• Quiero persuadir a mi amiga para que vaya...

Both are possible, but convencer sounds very natural here.

Because Spanish usually omits subject pronouns when the verb ending already shows who is doing the action.

• Quiero already means I want

So yo is not necessary.

You could say:

• Yo quiero convencer a mi amiga...

but that would usually add emphasis, contrast, or clarity.

For example:

• Yo quiero convencerla, pero él no. = I want to convince her, but he doesn’t.

In a neutral sentence, leaving out yo is normal.

The intended meaning is that your friend is the one you want to convince to go with you.

So:

• Quiero convencer a mi amiga de ir al festival de cine conmigo.

means you want to convince your friend to go to the film festival with you.

Grammatically, conmigo attaches to the idea of going, and in context it means she would go with me.

This is a normal Spanish way to express that idea.

Yes, that is also correct.

There are two common ways to express this idea:

• convencer a alguien de + infinitive
• convencer a alguien de que + subjunctive

So both are possible:

• Quiero convencer a mi amiga de ir al festival de cine conmigo.
• Quiero convencer a mi amiga de que vaya al festival de cine conmigo.

The first is a bit more compact. The second spells out the clause more fully with vaya.

Both are natural.