Non ho tempo di truccarmi stamattina.

Italian often leaves out the subject pronoun when it is already clear from the verb form.
Ho already means I have, so io is unnecessary unless you want emphasis or contrast.

• Non ho tempo... = normal, neutral
• Io non ho tempo... = I don’t have time... maybe contrasting with someone else who does

In Italian, non usually goes directly before the conjugated verb.

• Non ho tempo = I do not have time
• Non mangio = I do not eat
• Non posso venire = I cannot come

So non ho is the standard way to negate ho.

Because Italian normally uses the pattern:

avere tempo di + infinitive

This means to have time to do something.

So:

• ho tempo di mangiare = I have time to eat
• non ho tempo di studiare = I don’t have time to study
• non ho tempo di truccarmi = I don’t have time to put on makeup

For English speakers, this is one of those places where Italian uses di where English uses to.

Because when a reflexive pronoun goes with an infinitive, it is attached to the end of the infinitive.

• truccarsi = to put on makeup / to do one’s makeup
• truccarmi = to put on my makeup
• truccarti = to put on your makeup
• truccarsi = to put on his/her/their own makeup

So after di, you use the infinitive form with the pronoun attached:
di truccarmi

di mi truccare is not correct.

The base form is truccarsi, a reflexive verb.

Here is the breakdown:

• truccare = to make up, to apply makeup to someone
• truccarsi = to put makeup on oneself / to do one’s makeup
• truccarmi = to do my makeup

So -mi means myself here.

No. There is both a non-reflexive and a reflexive use.

• truccare qualcuno = to put makeup on someone
• truccarsi = to put makeup on oneself

Examples:

• La truccatrice trucca l’attrice. = The makeup artist does the actress’s makeup.
• L’attrice si trucca. = The actress puts on her makeup.

In your sentence, the speaker is doing their own makeup, so the reflexive form is needed.

Yes, basically. It is the reflexive pronoun for io.

Reflexive pronouns are:

• mi = myself
• ti = yourself
• si = himself/herself/yourself(formal)/themselves in some uses
• ci = ourselves
• vi = yourselves
• si = themselves

So truccarmi literally works like to makeup myself, though natural English says to put on my makeup or to do my makeup.

Stamattina is a very common adverb meaning this morning. It is often written as one word in modern Italian.

You can also say:

• questa mattina
• sometimes sta mattina in less formal usage

All mean roughly the same thing, but stamattina is very natural and common in everyday speech.

Yes. That is completely correct.

• stamattina = this morning
• questa mattina = this morning

The version with stamattina is a little more compact and conversational, but both are normal.

Yes. Italian word order is flexible, especially with time expressions.

For example:

• Non ho tempo di truccarmi stamattina.
• Stamattina non ho tempo di truccarmi.

Both are correct. The second version puts more emphasis on this morning.

Because avere tempo is the usual expression for to have time in a general sense.

• Non ho tempo = I don’t have time

Adding il is possible in some contexts, but it changes the feel and is less neutral here. In everyday Italian, non ho tempo is the standard way to say it.

The safest and most standard choice here is di:

• non ho tempo di truccarmi

That is the normal structure after avere tempo when it is followed by a verb.

You may sometimes hear per in some contexts, but for learners, avere tempo di + infinitive is the pattern to remember.

It does, but Italian expresses that idea differently. After many nouns, adjectives, and verbs, Italian uses di before an infinitive where English often uses to.

So:

• tempo di truccarmi = time to do my makeup
• felice di vederti = happy to see you
• decidere di partire = to decide to leave

English uses to, but Italian often uses di instead.

Yes, but it changes the meaning slightly.

• Non ho tempo di truccarmi stamattina. = I don’t have time to do my makeup this morning.
• Non ho tempo di truccarmi oggi. = I don’t have time to do my makeup today.

Stamattina is more specific than oggi. It refers only to the morning.

It is neutral, natural everyday Italian. Nothing in it is especially formal or informal.

• Non ho tempo... = normal spoken and written Italian
• stamattina = very common in speech and informal writing, but not wrong in standard Italian at all

So this is a very natural sentence for everyday use.