
happykj |
The young template is used to create young version of monster easily, so it shouldn't require additional calculation.
The rule of Young Character Creation also didn't mention there will be additional damage penalty for being young.
So the reduced damage should already include the adjustment of the weapon size (if it is using weapon).

Mysterious Stranger |

Logically it should only be for size and only when they are using appropriate sized weapons. There is no reason a young satyr could not use a medium longsword that did not deal reduced damage. They would be subject to all the rules on using an improperly sized weapon.
The template was designed so that a GM can quickly slap it on a creature and not have to do any work.

Azothath |
I am wondering if the reduced damage from the young template is due to being smaller or in addition to that. For instance, would a young satyr wielding a small longsword do 1d6 damage or 1d4?no, it is just a 'quick & dirty' method as it is a simple template. It has been used/abused in several published scenarios/adventures.
You should reduce manufactured weapon size by one category (scales different than size) otherwise you hit inappropriate weapon size penalties and may seek the few nonPFS legal feats to compensate.