Whatever covered in authenticated PurANas and Itihasas are to be taken as history based on actual happenings.
The Supreme Purusha is behind the prakriti as the nimitta and upAdAna kAraNa. The Deity is very important for us.
There is a subtle meaning as well in each avatAra for our understanding and practice .
All the avatAras of Gods are meant for our reflection, contemplation and learning.
In SrIVaishnAva tradition, SrI viSvaksena is worshipped. He is the Supreme Commander.
yasya dvirata vaktrAdyA: pArishadyA: paraSSatam !
vighnam nighnanti satatam viSvaksenam tamASraye !!
As far as SrI GaneSa:
He is GaNapati -- Lord of Demi-Gods
He is VinAyaka --- Leader par excellence.
He is VignarAja--- Remover of all obstacles
His big ears for open-mindedness -- Quality to listen to others--Answers the prayers of Devotees
KarNabhyAm bhUri Visruvam
Bhadram karNebhi: SruNuyAma deva:
His sharp eyes for grace --- a mix of Sun and Moon.
His Trunk for flexibility --- power to handle the heaviest and the subtlest things
His big stomach -- power to assimilate and digest varied forms of knowledge
MoshikaVAhana --- He makes the best use of available resources
He is Modakapriya --- Lover and bestower of joy
He is the bestower of Siddhi as well as Buddhi.
-----------And so on --------
Om MahA GaNapataye Namah !
durgAm vinAyakam vyAsam viSvaksenam gurUn surAn !
sve sve sthane tvabhimukhAn pUjayet prokshanAdibhi: !!
---- SrImad bhAgavatam