Competimos en cada ronda.

Because competir is an -ir verb. In the nosotros form, present-tense -ir verbs end in -imos:

• yo compito
• tú compites
• él/ella compite
• nosotros competimos

So competimos is the correct we form.

Also, competir is a stem-changing verb (e → i) in many forms, but nosotros does not change in the present tense. That is why it is competimos, not compitimos.

It can mean either one, depending on context.

For some -ir verbs, the nosotros form is the same in the:

• present tense: we compete
• preterite: we competed

So competimos can mean:

• We compete in each round.
• We competed in each round.

Usually the surrounding context makes it clear:

• Normalmente competimos en cada ronda. = We usually compete in each round.
• Ayer competimos en cada ronda. = Yesterday we competed in each round.

Because Spanish often leaves out subject pronouns when the verb already shows who the subject is.

Competimos already tells you the subject is we. So:

• Competimos en cada ronda.
  and
• Nosotros competimos en cada ronda.

both work.

Adding nosotros usually adds emphasis, contrast, or clarity:

• Nosotros competimos en cada ronda, pero ellos no.
  We compete in each round, but they do not.

Here en means something like in or during.

• en cada ronda = in each round

It shows the action happens within each round of the competition.

Using another preposition would change the meaning:

• en cada ronda = in each round
• por cada ronda = for each round
• a cada ronda = to each round

So en is the natural choice here.

Because cada is normally followed by a singular noun.

So you say:

• cada ronda = each round
• cada día = each day
• cada persona = each person

You do not pluralize cada here.

This is similar to English each, which also goes with a singular noun.

In this sentence, ronda means round, stage, or turn in a game, contest, or competition.

It is a feminine noun:

• la ronda
• cada ronda

Depending on context, ronda can mean other things too, such as:

• a patrol
• a round of drinks
• a circuit or round

But here the competition meaning is the one that fits.

Because stem-changing verbs in Spanish usually do not change in the nosotros form of the present tense.

With competir, the stem changes from e to i in many forms:

• yo compito
• tú compites
• él compite
• ellos compiten

But in nosotros, the stem stays the same:

• nosotros competimos

So competimos is correct, and compitimos is not the present-tense nosotros form.

Yes, and it would be very similar, but there is a small difference in feel.

• en cada ronda emphasizes each individual round
• en todas las rondas emphasizes all the rounds as a whole

In many situations, both can work. But cada often sounds a little more focused on one-by-one repetition.

Yes. Competimos en cada ronda sounds natural in Latin American Spanish.

There is no special regional issue in this sentence. The only thing worth noting is that Latin American Spanish generally does not use vosotros, but that does not affect this sentence because it uses nosotros.

A simple pronunciation guide is:

com-pe-TI-mos en CA-da RON-da

Stress falls on:

• ti in competimos
• ca in cada
• ron in ronda

In natural speech, competimos en may sound slightly linked together, almost like:

com-pe-TI-mo-sen CA-da RON-da

But the words are still separate.