A gap in the hole when inserting JIS square BB to a Truvativ Crank I push the BB inside a crank hole without any tool but I expect a few milimeters gap. 

The Truvativ crank definitely uses JIS interface, but the question is: DOES the gap make any problem? or is it normal?

some images:
If you have correctly tightened the crank bolt then this normal. The recommended torque spec is 305-390 in lbs. If the crank axle came all the way to the end you would run the risk of the bolt bottoming out before the crank was seated.