Learn French: La sentinelle ne bouge plus, elle dormira. - The sentry is no longer moving, she must be sleeping.

This is the "futur de probabilité" (epistemic future) that you are currently learning. In French, the future tense is often used to express a strong assumption, probability, or deduction about a present situation. By saying elle dormira, the speaker is guessing why the sentry isn't moving right now.

Could I use the verb devoir to say "she must be sleeping" instead?

Absolutely. You could say elle doit dormir, which is actually the most common way to express this in everyday spoken French. Using the future tense (elle dormira) for probability is completely normal but sounds slightly more literary or poetic.

Does the pronoun elle mean we know the sentry is a woman?

Not necessarily! The noun la sentinelle (the sentry or guard) is always feminine in French. Pronouns must agree with the grammatical gender of the noun they replace. Even if the guard is a man, you still refer back to la sentinelle using elle.

Why does the English translation use the continuous "is moving" and "sleeping" when French just uses simple verbs?

French doesn't have an exact equivalent to the English "-ing" continuous tenses. The present tense bouge can mean "moves" or "is moving", and the future dormira can mean "will sleep", "will be sleeping", or (as a probability) "must be sleeping". The context tells us this is an ongoing action.