As a general Islamic rule, it would be considered as a haram practice to touch the script of the Holy Qur'an with any part of one's body, without performing Wudhu. But in regards to your second inquiry that you asked
1) Can she read it on her phone,like touching the verses in her phone?
The response is that touching the Holy Qur'an through cellphones is
not considered as a haram practice. Since it would be touched
indirectly. In truth, that is the light/glass of the mobile phone that you
touch, not the real Quran.
In regards to your second inquiry that you asked
Note: As a significant point, when some women is in merses, she should not recite the verses which are Wajib-al-Sajdah (obligatory to Sajdah), even it some Marja'al taqlid declares that she ought no to recite all those Surahs (which have Wajib-al-Sajdah verses). Otherwise you can recite the rest of the holy Quran (except those 4 Surahs according to Shia's perspective)