She would have to have a fairly large estate to have any estate taxes due. If there are any estate taxes due, generally the trustee or the personal representative of the probate estate, if there is a probate estate in addition to the trust, would pay from the trust or estate assets before any distributions.
As for income taxes... Generally the distribution that you receive will not be subject to income tax. If the trust realizes enough income - interest, dividends, capital gains, royalties, etc. - while the trust is being administered, there is a possibility that some part of what you receive will be income. Even if there is some income, it is usually a small part of the distribution. But the trustee should be able to give you more information.