OK, Paul commence.

It is the third-person singular present form of the verb commencer.

So:

• commencer = to begin / to start
• Paul commence = Paul begins / Paul starts / Paul is starting, depending on context

Because the subject is Paul (equivalent to he), French uses commence.

Commencer is the infinitive, meaning to begin.

When French uses a conjugated verb with a subject, it changes form:

• je commence = I begin
• tu commences = you begin
• il/elle/on commence = he/she/one begins
• Paul commence = Paul begins

So commencer would only be used in places where English would use to begin, not begins.

It is the present tense: more specifically, the present indicative.

In English, this can match several ideas depending on context:

• Paul starts
• Paul begins
• Paul is starting

French often uses the simple present where English might prefer either simple present or present continuous.

Normally, no: as written, it is most naturally read as a statement:

• OK, Paul commence. = OK, Paul starts / Paul goes first.

If you wanted to speak to Paul and tell him to start, you would normally make that clearer with punctuation and intonation:

• OK, Paul, commence ! = OK, Paul, start!

So the presence or absence of a pause around Paul matters. In your sentence, Paul is most naturally the subject of the verb.

Because commencer can be used on its own.

So:

• Paul commence. = Paul starts / begins.

But if another verb follows, French usually uses à:

• Paul commence à parler. = Paul starts to speak.
• Paul commence à travailler. = Paul starts working / starts to work.

So à only appears when commencer is followed by another verb in the infinitive.

Yes. OK is very common in French, especially in spoken and informal language.

You will hear and see things like:

• OK
• ok
• okay

A more traditionally French alternative is d'accord, but OK is completely normal in everyday use.

It is pronounced roughly like koh-mahns.

A few important points:

• the co- sounds like ko
• the -mence part has a nasal vowel, so it is not pronounced like English mense
• the final e is silent

In IPA, it is /kɔ.mɑ̃s/.

Because Paul is a proper name. In French, proper names normally do not take an article in this kind of sentence.

So:

• Paul commence. = Paul starts.

That is completely normal word order:

• subject + verb

Because before e, the letter c already has the soft s sound in French.

So in commence, the c is pronounced like s automatically.

You see ç only when French needs to keep that soft sound before a, o, or u. For example:

• nous commençons

Without the cedilla there, c would sound hard. But in commence, no cedilla is needed.

Yes. In context, that can be a very natural translation.

For example, if people are deciding turn order, Paul commence often means:

• Paul starts
• Paul goes first

That is not a different grammar point; it is just the most natural English translation for that situation.