Say, I have 5 groups in FIM, Metaverse and AD. Now I want to delete one group from FIM and Metaverse, but want to keep the group in AD. Is that possible to achieve? With object deletion rule in the Sync Engine, when I delete a group from FIM, it is getting deleted from AD too.

Yes it is possible. You simply remove the deletion rule in AD MA. Under deprovisioning options, instead of "Delete connector on next export", choose "Disconect".

Under deprovisioning options, I do not see Delete connector on next export option. The options available are 1) Make them disconnectors 2) Make them explicit disconnectors 3) Stage a delete on the object for the next export run 4) Determine with a rule extension.

When I selected the option 3, a object got deleted from AD upon deletion from FIM. However, in the Metaverse i see a ghost object (without a displayName) after deletion. 

Sorry, I don't have a FIM in font of me, so I did not remember the exact syntax.  Option 3 is what you have and you need option 1.