Short answer: Yes, a man can perform Pooja even if someone in the home is menstruating. In Jainism there isn’t a scriptural rule that treats menstruation as a barrier to doing worship or to touching a puja items.

Key points to keep in mind:

• Jain philosophy emphasizes non-violence, truth, cleanliness, and respectful conduct. There is no concept of ritual impurity that makes a person unfit to perform worship just because a woman in the household is on her period.
• Both Digambar and Śvētāmbara traditions describe menstruation as a natural biological process. They do not prohibit men from conducting puja or from engaging in devotional activities due to a woman’s menstrual state.
• Practical etiquette (not a religious restriction) may be observed in some families out of personal or cultural preference—such as giving space, ensuring comfort, or maintaining cleanliness—but these are personal customs, not Jain doctrinal requirements.

Regarding “what activities should men not do when touching women in periods”: there is no Jain rule that forbids a man from touching a menstruating woman in order to perform daily duties or worship. Jainism would encourage respectful, non-harmful behavior toward all beings. If a family has its own comfort-based boundaries (for example, modesty or cleanliness practices), those can be followed as personal choice, but they are not mandated by Jain scripture.

If you’d like, I can share a simple, authentic Jain summary of how purity and conduct are treated in the relevant texts, or help you find a specific Jain scripture reference that discusses cleanliness and worship in Digambar and Śvētāmbara traditions.