Is it proper to obtain an Etrog from israel for the Sukkot after shmita? Are there special Halachot regarding the Arbah Minim during or after the Chag? I have always purchased my Arbah minim from israel, and would like to thisyear also.

An Etrog from Eretz Yisrael even though contains the Shmita Kedusha can be bought out of Israel and used during Succot [Igrot Moshe OC 5; 42] Since there is a prohibition to do business with Shmita fruit you should pay for the Lulav and Haddas enough to cover the cost of the Etrog as well [Rambam Shmita 8; 11] After Succot you can't dispose of the Etrog rather let it rot [or dry out] in peace and bury it respectfully, some hold the Etrog should find its way back to Israel however if it is not easily possible follow the previous advice.