does drag work with dawnstar i see it posted on the board a\

and cam she use her hss lite to base attack then use the msoe team abiltiy then run away

It will only work if she starts adjacent and rolls to breakaway. drag only works on a successful breakaway roll. So you could not use the automatic breakaway part of her SP that grants HSS option 1. Furthermore you need to use a Power Action to activate Drag. And then you could not use another action to activate the HSS Lite. If she uses Drag that about all she can do.

Drag 5 points
Sets:Legion of Super Heroes
Prerequisites : (Wing Speed)
Choose a character. Give the character a power action when it is adjacent to a target opposing character. If the character successfully breaks away, move the character up to half its speed value and then place the target in an unoccupied square adjacent to the character. If the target is not a flying character and occupied a square of elevated terrain, and then was placed in a square of grounded terrain, deal it 2 damage after being placed.
Errata:


I'm assuming you mean the feat: The Monster Society of Evil alternate TA for Superman Enemy TA:

The Monster Society of EVIL! Free
Sets:Crisis
Prerequisite: Superman Enemy Team Symbol
All characters with the Superman Enemy team ability have the following team ability instead: At the beginning or end of your turn (choose once per turn for all friendly characters with this team ability), roll a d6 for each character that has this team ability. On a result of 5 or 6, deal 1 damage to each opposing character adjacent to that character. A character can be dealt damage by this team ability only once per turn.
Errata:

This TA only works at the beginning or end of your turn. That means either before any actions you make with any figure, or after you make all your actions with any figure. It cannot be done between actions of different figures, and absolutely cannot be done in the middle of any one figures action.

Tarnish

thanks for the answer