I wouldnt consider him a baby, maybe a teenager or so. His fins are pretty full looking so Id say about 2 months. Ive seen some real baby looking ones at Petco that were about this big -------- including fins.
Its also normal for bettas not to eat when you first get them, just put in a few pellets like normal and remove them in a few minutes if he doesnt eat them. He should pick up on eating by the end of the week.
He is very pretty too even thought his tank is a bit girly, lol. You have some very interesting names too.