Here goes,to the best of my knowledge,I try to keep up to date.
1. Why I can't submit ink prints taken by a LEO
Because IL only accepts IL State Police approved LiveScan vendors to to submit prints.Sorry,it's part of the law,it's IL,.
2. What law or regulation forbids LiveScan from crossing state lines and why ?
I don't know of any law forbidding it,I think it's just that IL hasn't approved any out of state vendors.
3. How I can teach IL CCW, but not be able to get an IL CCW or carry there?
If your from out of state,and it's not one of the 4 approved states that qualifies you to obtain a $300.00 non resident permit,you must have a carry license from your state,along with all the other requirements to apply to be an instructor.
So it appears that you could apply for a non resident instructors license if you're from MD,if you have a MD carry license,like you said,then come to IL and get LiveScan printed .But if you teach the class to MD residents,or a lot of other states residents, they will not be able to get a license,unless the law changes.Remember it's IL,the people running this state have things so messed up this seems normal to them.