Depends on your MOS, but it will be in the lower 48. Infantry goes to Ft. Benning, Artillery goes to Ft. Sill, etc. There are no Basic Training posts in Alaska. You'll find out where you're to report to for BCT once you sign your enlistment contract at the Military Entrance and Processing Centre (MEPS).
Basic Training for Illinois National Guard is 9 weeks.
Basic training for Military Police (MP) in the National Guard is typically held at the U.S. Army Training Center at Fort Leonard Wood in Missouri.
The address of the Alaska National Guard Historical Holding-Museum Fund Inc is: Po Bpx 5800, Fort Richardson, AK 99505-9950
Training.
No, but as the former governor of Alaska was head of the National Guard there.
There is no Army National Guard basic training. It is basic training at one of the US Army's active duty training base. All active, reserve, and guard members train together as one. The platoon guide is basically a leader of the platoon.
No, but it is your responsibility to attend training with that state.
Hutchinson Air National Guard Base, located in Kansas, has not ended. It is currently operational as a training site and support facility for the Kansas Air National Guard.
In any State Guard/State Defence Force, the training is typically going to be more oriented towards Search-and-Rescue and CERT (Community Emergency Response Team) activities than actual tactical military training, in order to further facilitate the National Guard in their mission for the state. Most SG/SDF units I've known of have one weekend per month of training (for some units, it may only be one day of that weekend), and may or may not have an Annual Training period each year (typically, one week vs. the two weeks of the National Guard). Membership in these forces is voluntary, requiring one who volunteers to purchase their own uniforms and equipment, although members typically are paid when called up for state activation.
It is the other way around. What does the members contribute to the National Guard. The training that members receive from the guard helps the unit more effectively in having that persons motivation and skills achieve excellence. It also helps in promotions and additional training.
Depending on where the training is from, you accumulate points for promotion and retirement.
Each unit will be assigned to an armoury, and units out of that armoury will typically be from the immediate area. Each state has a National Guard (as does Puerto Rico).