Beijing Capital Airport T3 to subway to Beijing South HSR

About the transportation, you need to take Airport Express to Dongzhimen first. Then take metro line 2 to Xuanwumen Station and transfer to metro line 4 to South Railway Station.
You can purchase the ticket at the Airport Express service counter at PEK. The detailed English signs that can help you find the places easily.

Do I just buy a ticket once going from Dongzhimen to Beijing South HSR, or do i have to buy a ticket each time i transfer from another T line?

Is the Airport Express free of charge? did you say i can purchase DONGZHIMEN to BJ SOUTH subway ticket at the Beijing Airport?

You can take subway from Dongzhimen to South railway station, so just buy the ticket once. It is not free. You need to buy the ticket at Dongzhimen station.