How to get this information

1. How to know if the owner's L$ balance is enough to pay or not?
2. Or how to know how much the owner paid by llGiveMoney(owner,amount) if the L$ balance isn't enough to the amount?

Basically, you can't do either as far as I'm aware, so if you have any sort of money-giving script you should always make sure that it is owned by an avatar with enough money.

If you are concerned about running out, you could always hardcode a money limit which you _know_ the av will be able to pay, and when it runs out of money, shut down the script. So, say, something like:

integer gFunds = 5000; // how much that av wants to pay out, at most
integer AMOUNT = 100; // the amount to be paid each time

// returns TRUE if the funds will allow another payment after that
integer pay(key id)
{
   llGiveMoney(id, AMOUNT);
   gFunds -= AMOUNT;
   return (gFunds >= AMOUNT);
}


default
{
   state_entry()
   {
      llSetText("Touch for money", <1.0, 1.0, 0.0>, 1.0);
      llRequestPermissions(llGetOwner(), PERMISSION_DEBIT);
   }

   touch_start(integer n)
   {
      if (!pay(llDetectedKey(0)) state out_of_money;
   }
}

state out_of_money
{
   state_entry()
   {
      llSetText("Sorry - out of money!", <1.0, 0.0, 0.0>, 1.0);
   }
}

If there are multiple payout amounts, you'll have to set the threshold to be the maximum amount that you might have to pay (or assume that there will be a _little_ more money available to cover the excess over the funds limit).

you could also know the initial balance of the giver, and track it inside the script, storing the current balance in the object description.

But how could I know the initial balance of the owner if the owner isn't me ?

You can't. You shouldn't. We wouldn't want you to be able to. Basically, design your system differently.