Mosfet bootstrap voltages
Is it 20 volts ? Bad because Vgs max is 15v. Or does it see 10 volts ?
  (20v pump - 10v source = 10v gate ?)
  
  And if it sees only 10v, why or how ? I ask why, because i dont
  understand why its 10v even though im applying 20v.


The gate will be at 20 volts and the source will initially be at 10 volts. That's a gate source voltage of 10 volts and within spec. Voltages are always relative.


  Second question: Would it be still 10v at the gate if i use an
  external 20v battery with no common ground. + of the battery to the
  gate and - to the source ( which is at 10 volts )


If you apply a 20 volt battery between gate and source then you have a problem irrespective of what other circuitry is raising the source to whatever potential.