No quiero resbalar otra vez en la acera mojada.

Because after quiero (I want), Spanish uses the infinitive of the next verb.

• quiero = I want
• resbalar = to slip

So:

• Quiero resbalar = I want to slip
• No quiero resbalar = I don’t want to slip

You would not say quiero resbalo, because resbalo means I slip, and Spanish does not normally put a fully conjugated verb after querer in this structure.

In Spanish, negation usually goes directly before the conjugated verb.

• Quiero resbalar = I want to slip
• No quiero resbalar = I don’t want to slip

This is very standard in Spanish:

• No tengo dinero = I don’t have money
• No puedo ir = I can’t go

So no comes before quiero, not before resbalar.

Not exactly.

• resbalar = to slip
• caerse = to fall down

You can resbalar without fully falling. For example, your foot slides on a wet surface. Sometimes slipping leads to falling, but the verbs are different.

So this sentence focuses on slipping, not necessarily ending up on the ground.

Yes. Otra vez and de nuevo can both mean again.

• otra vez = again / one more time
• de nuevo = again / anew

In this sentence, otra vez is very natural and common in everyday speech:

• No quiero resbalar otra vez = I don’t want to slip again

Using de nuevo would also be correct:

• No quiero resbalar de nuevo

Both work, but otra vez often sounds a bit more conversational.

Spanish usually uses en for being on or in a place in many everyday contexts where English uses on.

So:

• en la acera = on the sidewalk/pavement

Even though English says on the sidewalk, Spanish normally says en la acera. This is a very common difference between the two languages.

• Estoy en la calle = I’m on the street
• Está en la mesa can mean It’s on the table

So en la acera mojada is the natural choice.

Yes, acera is the normal word in Spain for sidewalk or pavement.

This is an important regional vocabulary point:

• In Spain, acera = sidewalk / pavement
• In some parts of Latin America, you may also hear banqueta, vereda, or other regional words

Since you asked about Spanish from Spain, acera is exactly the right word here.

Because mojada describes acera, and adjectives in Spanish must agree with the noun they describe in gender and number.

• acera is feminine singular
• so the adjective must also be feminine singular: mojada

Examples:

• el suelo mojado = the wet ground
• la acera mojada = the wet sidewalk
• las aceras mojadas = the wet sidewalks

So mojada agrees with acera.

Here it means wet in the physical sense: covered with water or made slippery by water.

• la acera mojada = the wet sidewalk

The verb behind it is mojar = to wet / to make wet.
The adjective mojado/mojada means wet.

In this sentence, it suggests the sidewalk is slippery, probably because of rain or water.

Yes. Resbalar en is a normal way to say to slip on a surface.

• Resbalé en el hielo = I slipped on the ice
• No quiero resbalar en la acera mojada = I don’t want to slip on the wet sidewalk

English learners may expect a different preposition, but en is natural here.

You could, but it changes the meaning slightly.

• No quiero resbalar otra vez... = I don’t want to slip again...
• No quiero caerme otra vez... = I don’t want to fall again...

If the important idea is that the surface is slippery and you don’t want your foot to slide, resbalar is better.
If the important idea is ending up falling over, caerme is better.

Because Spanish often omits subject pronouns when the verb form already makes the subject clear.

• quiero already tells us the subject is I
• so (yo) no quiero resbalar... and no quiero resbalar... both mean the same thing

Spanish usually leaves out yo unless you want emphasis, contrast, or clarity.

For example:

• Yo no quiero resbalar, pero tú sí quieres intentarlo.
  = I don’t want to slip, but you do want to try it.

In your sentence, yo is unnecessary.

A broad pronunciation guide would be:

No KYE-ro rez-ba-LAR O-tra beth en la a-SE-ra mo-HA-da

A few Spain-specific notes:

• quiero: the ie sounds like ye in one syllable: KYE-ro
• z in vez is pronounced with the th sound of thin in most of Spain
• c before e in acera is also usually pronounced like th in most of Spain
• j does not appear here, but mojada has j? Actually it does: mojada. That j is a strong throaty sound, not an English h, though English speakers often approximate it with h

So in much of Spain:

• vez ≈ beth
• acera ≈ athera
• mojada ≈ mo-HA-da

This is the most natural and neutral order:

• No quiero resbalar otra vez en la acera mojada.

Spanish word order is somewhat flexible, but changing it can shift the emphasis.

For example:

• No quiero resbalar en la acera mojada otra vez.

This is still understandable, but it may sound slightly less natural unless you specifically want to emphasize again at the end.

So the original version is a very good standard phrasing.