1) Would touching a girl break the fasting?2) Would shaking hands with a girl make one have to repeat Wudu?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Touching a woman does not break ablution if there is no ejaculation. If there is ejaculation, the fast becomes null and therefore making up that day becomes an obligation considering the sacredness of the month of Ramadan. Know that touching a Non-Mahram woman is forbidden for the Hadeeth of the Prophet : “If one of you were to be stabbed in the head with an iron needle it would be better for him than touching a woman whom he is not permitted to touch.” [At-Tabaraani from Ma'qal ibn Yasaar]

Shaking hands of a Non-Mahram woman is forbidden according to the agreement of Muslim scholars of the four schools of jurisprudence and others. Touching a Non-Mahram woman even with a barrier is also forbidden.

In addition, touching a woman or shaking hands with her without barriers and with sexual desire nullifies ablution according to the majority of Muslim scholars. It is also said that only touching with sexual desire does not break ablution as long as there is no ejaculation.

However, acting according to the first opinion is safer because it is sounder and the majority of scholars are of that opinion.

Allah knows best.