Firstly : Ganesh Chaturthi, is celebrated as a birthday (actually rebirth) of Lord Ganesha, as it is celebrated on fourth day of the bright half of Bhadrapad, it has a term Chaturthi in it.
The rebirth, as I mentioned, corresponds to the incident where while Ganesha in a human head form tried to block passageway of Lord Shiva, resulting in rage of Shiva and loosing his head. Thereafter, when Lord Shiva was consolidated by Devi Parvati, Shiva gave him a new birth attaching an elephant infant's head.
There is not ancient norm related to this celebration, according to latest date, this started from Shivaji's Time 1630-80, after that followed by Peshawars, from 1740-1820, thereafter it started loosing its glory when it was again renewed by Lokmanya Tilak in 1893, in contribution to unity of different castes and generate patriotic zeal among people against the British.
Secondly : Your second part has nothing to do with Ganesh Chaturthi. It is normal priviledge in Hindu households, to not celebrate till 1st year of relative's death, you cannot even worship (pooja, but you can inchant mantras) till the third day of relative's death. This has a more wider reference, which I don't think liable here, you can ask this question differently.