Is the text written correctly?

Your text is grammatical.

But perhaps it would be better to say:

The teacher should act as a prompter if an activity is not going smoothly.
If the student gets lost or cannot think of what to say next, the teacher should help them by offering some discrete suggestion.

Here I use "the teacher" and "the student" to signal generic reference.

I suppose that both options are correct, but which one seems more logical to you (in terms of using the articles)?

Discrete or discreet?

In the book it is written 'we may be able to help students by offering discrete suggestions'.

A very common error is to confuse these two words.

discreet adj. Showing discernment or judgement in the guidance of one’s own speech and action; judicious, prudent, circumspect, cautious; often esp. that can be silent when speech would be inconvenient.

discrete adj. Separate, detached from others, individually distinct. Opposed to continuous.

Thank you for clarification. I corrected that.