1. What is the exact difference between hard attack and soft attack?
Soft and hard attack represents the weapons that are used to take on infantry and armor. Soft attack represents small arms, rifles, machine guns, mortars, etc. While Hard attack represents anti tank weapons, AT launchers, recoil less rifles field guns. Personally these values aren't the most important. Just remember to keep up with the times, use 1942 inf in 1942, and you should be fine. The real question is in hardness, when making divisions try to lower their softness value as typically the enemy will be able to do much more soft damage then hard damage.
2. At what distance do HQ's give their bonuses? Can they give bonuses to units just in neighbouring provinces, do they have to be in the same province or do they have to be a part of the unit itself?
HQ give their bonuses to neighboring provinces and the same province. They do not have to be in the unit itself, in fact I like to leave the HQ as a separate unit to speed across the region and provide bonuses were needed.