When the Draft occurred in WW2 and all fit men were drafted in, what happened to the lawyers and doctors, were they given Officer training and officer ranks, unlike those without an education and became an enlisted? I saw Mad Men and one of the characters who was also a Doctor, was promoted to Captain immediately after training.
Did lawyers go into JAG Corp (but I'm sure it wasn't created until the 50s) and were Doctors highly sought after? Perhaps Doctors were drafted and placed as those examiners for checking the draft's health?
Also, since the oldest age to be drafted was 45, what if you were a congressman, senator, prosecutor or a Judge below that age, could you still be drafted and required to go?
Doctors in the US Armed Forces almost always enter with the Rank of Captain if they are operating in a medical capacity. It has been the base line rank. This is fairly common across all armies as well, for example, in the German cavalry units, Veterinarians were immediately promoted to Hauptmann (equivalent to a Captain) - as mentioned by Yerger in his Riding East.... Most media has actually surprisingly gotten this correct; MASH being most prominent in my mind.
Did lawyers go into JAG Corp (but I'm sure it wasn't created until the 50s)
No. They most often became officers however, across various branches. The actual rank did not always correspond to their civilian prestige, for obvious reasons of military merit. That being said, Lawyers generally made good Officers, and some of the most prominent company commanders in the US 2nd Armored Division for example, were lawyers stateside. James M. Burt, a civilian lawyer, earned the Medal of Honor leading a task force around Aachen, for example, and generally had an exemplary record (Source: Donald Houston). Lawmakers were often junior officers as well, and prior to the official entry of the United States into WWII many Democratic and Republican congressmen activated their reserve commissions to help prepare and train the AGF. Hoffmann's Through Mobility We Conquer, in describing the Mechanized Cavalry and Armored Corps' rise to prominence in 1940, mentions at least one Republican Congressmen who activated his commission as a 1st Lieutenant just so he could observe on-staff with the V Corps. Subsequently, he was able to argue for funding for the force in Congress, and served on-staff with various Corps for the duration of the war.
Also, since the oldest age to be drafted was 45, what if you were a congressman, senator, prosecutor or a Judge below that age, could you still be drafted and required to go?
I've already addressed this a bit, but it truly depended on what rank you held. If you were entering the military, or already held a commission, being a 2nd or 1st Lieutenant, or even a Captain at such an age would probably have you drummed out. It was only in highly unusual cases that men of excessive age were kept in, even in the General ranks.