Learn Russian: У неё очень слабый пульс, она может потерять сознание. - She has a very weak pulse, she can lose consciousness.

You can combine a verb like доработаться (to overwork oneself to a bad state) with the preposition до + genitive. The noun phrase for losing consciousness is потеря сознания. So you could say: Она доработалась до потери сознания (She overworked herself to the point of losing consciousness).

Why is there no есть in У неё очень слабый пульс?

When describing a specific quality of something that a person naturally possesses (like a pulse, eyes, or a voice), Russian omits есть. Adding есть here would sound as if you are confirming the mere existence of her pulse, rather than focusing on the fact that it is weak.

Потерять сознание translates literally to 'lose consciousness'. What is the everyday Russian equivalent for 'to pass out' or 'to faint'?

A very common everyday phrase is упасть в обморок (literally 'to fall into a faint'). Both are widely used, though упасть в обморок is slightly more conversational, while потерять сознание can sound just a bit more clinical.

Why use the perfective verb потерять here instead of the imperfective терять?