Tickle your brains...

123456
Across
  1. 3. Platform originated from leading city state
  2. 5. Uma, Soma have this additional responsibility!
  3. 6. Ertwhile ATM
Down
  1. 1. Keller und Knappich Augsburg (Apply the same logic as another hint!)
  2. 2. Hemodynamic recording
  3. 4. Join the firsts and think! : G-Lion-In-Xamarin