There are no fees for depositing Bitcoin from a third-party wallet onto your Abra wallet.
There are no fees for sending or receiving Bitcoin between Abra wallets. However, there is a network fee whenever a conversion from Bitcoin to another currency, or vice-versa is done.
Withdrawing Bitcoin from your Abra wallet onto a third-party wallet will incur a network fee (this fee is required to ensure your transaction is confirmed by the bitcoin mining network) and fluctuates based off of volume on the network. Abra does not profit from it.
For further information regarding Abra's fees, click here.