For your first question, She can learn and recite from her memory but she cannot touch the mushaf till she is pure.You can read from a book which has the tafsir or the translation of the meaning as this is not considered to be Mushaf. You can also read it from the mobile or the computer.
Reply to your second question, it is not permissible for any one joining the congregation late to bring someone behind from the earlier rows to join you in a back row.