Answer:  The obligatory Tawaf al-Ziyarah would be the main issue for a menstruating woman. If she is on her menses on the 10th of Dhul Hijjah to the time she has to travel, this would be a problem as she has to be in a state of purity to do the Tawaf.

No, we can’t say it’s preferred to avoid one’s menses in order to do more ‘ibadah; menses are a natural occurrence and avoiding what must be avoiding during menses is worship itself.

Answer:  A woman on her menses is prohibited from entering any masjid, this would include the Prophet’s Mosque, (peace and blessings of Allah upon him).

Answer:  Sunblock that has no scent/perfume is permissible.

BarakAllahu feek, please remember us in your duas during your blessed journey, may Allah ta’ala make it easy for you and blessed.