אני מבטיח שאבוא בזמן ולא אשכח את הכרטיס.

Yes. מבטיח is the masculine singular present form of להבטיח. In Hebrew, the present form is often used where English uses the simple present, so אני מבטיח means I promise.

If you wanted I promised, you would use הבטחתי. If you wanted I will promise, you would use אבטיח. But in this sentence, the act of promising is happening now, so אני מבטיח is the natural choice.

A woman would say:

אני מבטיחה שאבוא בזמן ולא אשכח את הכרטיס.

Only מבטיח changes to מבטיחה. That is because Hebrew present forms usually show gender. The future verbs אבוא and אשכח stay the same, because first-person singular future does not change for masculine vs. feminine.

The ש־ means that.

So:

• שאבוא = that I will come
• literally: ש + אבוא

In Hebrew, this ש־ is attached directly to the next word, so it is written as one unit.

Hebrew usually does not use a separate helper word like English will. Instead, the future meaning is built into the verb itself.

So:

• אבוא = I will come
• אשכח = I will forget

The beginning of the verb helps show the person. In future tense, א־ often marks I.

Because the verb forms already tell you the subject.

• אבוא already means I will come
• אשכח already means I will forget

So Hebrew often leaves out the pronoun when it is not needed. You could add אני for emphasis, but in a neutral sentence it is usually omitted.

Because לבוא בזמן is the normal Hebrew expression for to come on time.

This is a good example of prepositions not matching word-for-word between languages. English uses on, but Hebrew uses ב־ here. So it is best to learn בזמן as a fixed expression meaning on time.

It breaks down like this:

• ו־ = and
• לא = not
• אשכח = I will forget

So ולא אשכח literally means and not I-will-forget, which in natural English is and I won’t forget.

For ordinary negation in Hebrew, לא is the usual word. A different word, אל, is mainly used for negative commands, such as אל תשכח = don’t forget.

את marks a definite direct object. It does not have its own English translation here.

Since הכרטיס means the ticket, it is definite, so Hebrew uses את:

• אשכח את הכרטיס = I will forget the ticket

If the object were indefinite, Hebrew would usually leave out את.

• הכרטיס = the ticket
• כרטיס = a ticket or just ticket, depending on context

So את הכרטיס suggests a specific ticket, probably one that both speaker and listener already know about.

Yes. A very natural alternative is:

אני מבטיח לבוא בזמן ולא לשכוח את הכרטיס.

That means I promise to come on time and not to forget the ticket.

Both versions are good Hebrew:

• אני מבטיח שאבוא... = I promise that I will come...
• אני מבטיח לבוא... = I promise to come...

The version with ש + future sounds a bit more explicit, while the infinitive version is a bit more compact.