Is there an actual "Issur" of a girl joining the Israeli army. Especially in today’s age where girls don’t neccesarily have to go on the front line or even fight but to help in offices with paper work. What are the Halachic obligations and or problems with a Dati girl joining the army?

I don’t know of even one rabbi of any circle that will Halachacly permit girls army service. The issues are mainly the fact she is forced to be under the authority of males not of her family which is a violation of the laws of Tzniut, and the secondary fact that the spiritual risks for girls in the current army environment are very high (as proven time and time again).