אנשי עיר קטנה relate to a big city next to them as 4 Amos.

1.   ?    True.
2.   ?    False.
3.   ?    Only as far as measuring.
4.   ?    Only as far as Shevisah. (ie Placing an Eruv Techum there)
5.   ?    Teiku.

A town situated on the banks of a river requires a Dakah.

1.   ?    True, any size.
2.   ?    True, 4 Tefachim.
3.   ?    True, 4 Amos.
4.   ?    False.
5.   ?    Machlokes B&C.

One places his Eruv in a cave where does he start counting 2000 Amos from?

1.   ?    His Eruv.
2.   ?    The end of the cave.
3.   ?    The end of the cave if it is inhabited,
4.   ?    Machlokes A&B.
5.   ?    Machlokes A&C.

If one placed an Eruv in a deserted city, he has only 2000 Amos from the Eruv.

1.   ?    True.
2.   ?    False, he has only 4 Amos.
3.   ?    False, he has 2000 Amos from the walls around the city.
4.   ?    Machlokes A&B.
5.   ?    Machlokes A&C.

** Hadran Alach, 'Keitzad Me'abrin'! **

1.   ?    !!!!TRUE!!!!

If a Yisrael lives in a Chatzer with a Nochri he may not carry on Shabbos.

1.   ?    True.
2.   ?    False.
3.   ?    Unless there is no need for an Eruv. בישראל אחד
4.   ?    Even if there is no need for an Eruv. בישראל אחד
5.   ?    A, Machlokes C&D.