1. The Berserker Sword limits Frenzy to the bearer. However, a unit can get Frenzy from the Altar of Khaine (BRB p. 124) - and perhaps some Army specific magic.
Edit: note however that even when not itself subject to Frenzy (BRB p. "a unit that includes one or more Frenzied models cannot choose to restrain pursuit if it beats a foe in close combat. It will either pursue (if the enemy has fled) or overrun (if the enemy was wiped out in combat)"
2. BRB p. 105:
If you use a weapon or spell that uses a template against a monster mount, both the riders and the mount are automatically hit if the monster's base is touched by the template (note that this includes bouncing cannonballs!).
3. Regiments and Detachments are still independent units, albeit with special rules. In previous editions, the Detachment could make a Supporting Charge in the flank (if it had LoS and enough Movement) - this does not exist anymore. To "support" a charge by the regiment, the Detachment must have declared a charge itself and roll seperately.
The Detachment can still execute a Counter Charge, if the Regiment has been charged.
4. No.
