1) Are the Baby's allowed to play the Elam card?
Yes they can, there is nothing in the rulebook saying they can't. Thematically the Babylonian king has aquired an alliance at some sort of fabulous stroke of luck/large gift. (However, see here for a suggested variant to prevent gamey play)
2) If movementpoints are left after a regroup, may the same army move/attack again?
Yes, until they run out of movement points.
3) Does someone, have a clear example how piracy works, I don't understand the 1 or 2 costs difference?
Let me have a go. There are two different potential deductions to your income.
- The $2 penalty is paid if a player has a port under their control that is connected by sea to a pirate counter. This penalty is binary, if you have a port connected to a pirate counter you pay $2, it doesnt matter how many pirate counters your ports are connected to.
- The $1 additional penalty is if you have to use a sea route to connect back to your capital. For each pirate counter on a sea route that you use in this way, you lose 1$. If multiple ports use this sea route to trace back to their capital you only pay the penalty once.
As an example, say the Hittites control Troy and Hindawa, but due to some Arzawan activity cannot trace a land route back to Hattusa. There are two pirate counters on the sea route to the west of Alashiya. When the Hittites calculate income;
1) They must pay $2 because both Hindawa and Troy are connected to a pirate counter. It doesnt matter that there are 2 counters, and it doesnt matter that there are two cities connected to them. It is just a base $2.
2) Because they must use the sea connections to trace back to Hattusa they must pay an extra $2 (one for each counter). You pay for the route once, not per city. Both Troy and Hindawa can use the route paying the cost once.