Re: Shed antlers
Actually Baga Yaga's house is a shed. Pushkin says it quite clearly:
<<избушка там на курьих ножках стоит без окон без дверей>>
(There a shed without windows or doors stands on chicken legs)
избушка (izbushka) is a diminutive of изба (izba), a (wooden) hut.
However, the presence or absence of antlers is not reported by Pushkin, who is more concerned to let us know that Baba Yaga flies around in a mortar (and not on a broomstick).