On any game not linked with Facebook (i.e., on the SQ-Network ), removal of friends is possible. For more information, see Neighbor Removal .
I'm not receiving any gifts from my neighbors
There are two potential causes for this issue:
Your neighbors have "gifts for sending" to give but are not sending them to you. There are a variety of reasons why-- they may not have any "gifts for sending" that are on your wishlist; they may not be playing; they may just be unsupportive; etc.
Your neighbors are not receiving any "gifts for sending" and cannot send any to you. If you are playing on the SQ-Network they may be suffering from a known issue
I'm not receiving any gifts to give to my neighbors
There is a known issue that has been reported to Social Quantum since Feb 2013 that players are not receiving "gifts for sending" every 8 hours as posted on the official FAQ.
see When am I eligable for free gifts in the game?