1. Is iddah compulsory while the wife and husband are leaving in different countries from last five months?
2. Is the obligation to provide for the ex-wife is still applicable when wife demands divorce from her husband and if she is earning?
3. Should the husband demand whatever given to wife except mehr in the above case?
The iddah seems to be intended for two purposes: to ascertain pregnancy and to give a chance of reconciliation. For the couple living separate the first point may be ignored but the second remains operative. Besides the laws given by the Almighty are important in form and spirit. If we believe that the underlying reason of an active is no more operative in a case yet we should follow the form. Therefore, I would say that iddah is compulsory for this couple.
Since the Islamic Shari'ah takes it for granted that the husband is responsible for the provision if the woman demands he has to provide her during the iddah. If she forgoes it then there is no problem. This applies to both the earning and the non-earning wives.
The husband is encouraged by the Almighty not to demand and take back anything from the wife. As for mahr this is her sole ownership unless she pays it back to free herself of the bond when the husband is not willing to divorce her. The gifts too should not be taken back unless the woman has committed violations of the divine laws regarding sexual behavior.