No. Whilst a unit with Random Movement can move into base contact with an enemy unit during the Compulsory Moves sub-phase, Arcane Urgency causes units to move when the spell is cast, during the Remaining Moves sub-phase.

Earthen Ramparts does not prevent a unit from declaring a charge, it prevents it from charging. In other words, yes the unit must declare a charge if obliged to do so. However, because the unit cannot charge, it does not move at all and the charge is failed.

No.

Yes. A unit upon which Earthen Ramparts has been cast counts as being behind a defended low linear obstacle when charged. Think of the spell’s effect as representing a magically manifested obstacle, rather than a physical terrain feature.

No. Weapons limited to a single attack can only inflict a single hit.

The spell is cast at the Wizard's Initiative, meaning attacks generated by the spell are made at the Wizard's Initiative. However, if the casting Wizard wishes to use a weapon with the Strike Last special rule, those attacks are made at Initiative 1.