I checked the site few days back (a week ago IIRC) when they were charging 0.0001 btc in fee for withdrawal, it changed to 0.0003 btc 3 days ago and is 0.0002 btc right now. Is there a dynamic structure in place which changes the fee according to the price of btc or is it based on the minimum that is required to get included in a block soon?
Yes, It almost happens in Stake. If you have noticed on your Transaction ID then you will see that the total subtracted amount is actually mining fees,
stake does not take any commission from here, 0.0001/0.0002/0.0003 the full amount is going as mining fees to seed up your first confirmation.
and as well withdrawal fees are changed on the basis of the price,
As far as I know, they just cut the next block fees, So that your transaction is mined on the next block, maybe it will take less than 10 minutes to be confirmed.