Can my car leak oil if the oil I used is too thin? Will it cause damage engine?

See owners manual for proper oil specs! The shield under the engine is catching the oil and will spill over when parked on a slope. Not so "when it is parked flat" but it will eventually! Have the leak checked to find the source. NOW, incorrect oil, or worse NO oil, will absolutly damage the engine!! Best find the leak and change the oil.