Your understanding of the word 'शायद' is right. It does mean maybe/perhaps/probably. The writer isn't sure about what is सिद्धेश्वरी looking at and that's the reason the word 'शायद' is used. She is either looking at her toes or the ants crawling on the ground.

yes, you are correct. 'perhaps/maybe' she looked at toes or moving ants on the floor. writer do not know for certain what she started doing after putting off the choolha. सिद्धेश्वरी ने खाना बनाने के बाद चूल्हे को बुझा दिया और दोनों घुटनों के बीच सिर रख कर शायद पैर की उँगलियाँ या जमीन पर चलते चीटें-चीटियों को देखने लगी। After cooking food, Siddheshwari extinguished the choolha and putting her head between both the knees perhaps/maybe started looking to toes or ants moving on the floor.

Both are correct. "Shayad" :-)

Here शायद mean "May be"