I've question regarding marriage. one woman taken Kula from her husband 4 yrs back but , the person who recited Kula was a Sunni mulavi, if she want to marry another person , is she has to go through diverse process (Kuala/ Talaq by Shia aalim ) and have to observe idda period?.

For taalaq/khula there are few conditions if those are not applied then it is not valid.
1-proper Segha should be pronounced and two Adil(just) people will witness (here it is missing) and woman should be in the state of taharat (not seeing her menses at that time)
If all conditions were present then khula is valid then she has to go for Iddah(period of three months)