Another partial answer:

Across

1.

2. Gaul

3. Concern

4. Femme

5. Habit

6. Resident

7. Taboo

8. Exhale

12. Oily

Down

1. Exploit

3. Poland

4. Date

5. Agent

6. Alms

7. Kabul

8. Diet

12. Oolong

13. Mesa

Another partial answer:

Across

2. Gaul

3. Concern

4. Femme

5. Habit

6. Resident

7. Taboo

8. Exhale

12. Oily

Down

1. Exploit

2.  

3. Poland

4. Date

5. Agent

6. Alms

7. Kabul

8. Diet

9.  

10.  

11.  

12. Oolong

13. Mesa