I was curious how the progress worked exactly. If I get six checks in combat training, can I spend several EXP and learn multiple skills, or do I have to get to six checks each time I want to spend an EXP?
Don't make up rules or add qualifiers, just read the tracking sheet:
"As long as six progress is marked in combat training, you may learn any of the following skills - archery, brawling, dueling, or military - at a cost of one experience per skill. You may learn a new skill at any time."
So yes, you may learn multiple skills by spending several experience and no, you do not have to start over with your training.