score:7
Can a valid US visa in the old passport (MRP) be transferred to new passport (electronic)?
No. A new visa can be issued in the new passport, but this is not necessary. She can also use the visa in the old passport along with the new passport.
If she carries two passports with her during travel (old one with valid visa and new one), will the difference in type (one is machine readable and another is electronic) cause any issue during travel in the airport?
No. Sources note that the passport must be of the same "type," but this refers to the categorization of the passport as a normal passport, official passport, or diplomatic passport. Whether the passport has an RFID chip or not isn't relevant.
Given this case, does she need to apply for new US visa? Her US visa still has 2 years validity.
It is not necessary to apply for a new visa in this case.