Drana's last ability triggers after combat damage has been dealt, so only attacking creatures that survive the combat damage step in which Drana deals combat damage will have +1/+1 counters put on them.

The +1/+1 counter won't change how much damage Drana or any other attacking creature with first strike or double strike deals during that combat damage step. However, the +1/+1 counters that are put on attacking creatures without first strike will affect the damage those creatures deal during the regular combat damage step.