accept the Daleks in the episodes army of ghosts and doomsday there was only 1 and that was the time war. The Daleks were in need of help and asked for the Cybermens help and the Cybermen accepted. Infact when the Sontarans tried to enter the war and were disallowed they tried to inflict a surprise attack on the Cult of Skaro ( Dalek sec, jast, caan, thay) which the Cybermen countered attacked and saved the Daleks from destruction.
Yes there were. The Cyber Wars of the 26th century were fought between Cybermen and humans, maybe even other species. The war is not shown directly on the show but the plots of "Revenge of the Cybermen" and "Earthshock" revolve around the conflict. If you mean Cybus Cybermen, however, no wars yet that we know of - and the previous asnwer about the Time War is untrue.
The first answer, concerning the Time War, is certainly not from any televised BBC sources. There has never been any suggestion that the Cybermen were in any way involved with or even aware of the Time War. From the Dalek attitude to the Cybermen in "Army of Ghosts"/"Doomsday", the Daleks would not have asked for help from the Cybermen and would not have thought the Cybermen capable of providing any help. There's also never been any suggestion that the Sontarans even suspected the existence of the Cult of Skaro.