Are their degrees of priesthood power? The Savior said that if we had the faith as a grain of a mustard seed that we could move mountains. In my mind he has set the bar or standard. If we have faith less than the grain of a mustard seed then it tells me that we have less power and could not move mountains. Is it the lack of power (faith) that stops us from being successful in giving a blessing?
There’s a bit of a misunderstanding that often occurs when we discuss priesthood power. When we, as men, receive the priesthood, we are not bestowed with the ability to perform magic. We are not Harry Potter.
As you rightly point out, the power to move mountains, heal, and perform miracles, comes by faith. And anyone who has this faith may rightly perform said miracles. Miracles are performed by the power of the priesthood, but it is God’s priesthood that performs them, not ours. We simply exercise faith in God.
In this regard it can get a bit confusing, but is fairly straightforward, if we break it down. When we refer to the priesthood power, there are two distinct meanings implicit. The first is meaning the power of God. All of God’s power is the priesthood. By it the earth and all things therein were created. And by it all miracles are performed. The second meaning is related to the power given to man when he has the priesthood conferred upon him. This power is not just the power to perform miracles (although that does accompany it ofttimes). As pointed out, a man already had the power to perform miracles by faith (or, rather, God already has the power to perform miracles according to a man’s faith). So what power is given when the priesthood is conferred?
The power to save souls through performance of the ordinances.
In other words, the power and the authority of the priesthood are one and the same when it comes to having it conferred upon us. And in this regard, yes, there are levels to the power. A priest has the power to baptize. A priest does not have the power to confer the Holy Ghost upon someone.
It does get a bit more complicated because there are certain acts that are authorized for priesthood holders to perform such as blessing the sick. Men who hold the priesthood are currently specifically authorized to lay their hands on the sick and to use the priesthood they have been given to pronounce blessings of healing. But the power of these healings, as you indicated, comes from faith, and generally from the faith of those receiving the blessings.
Neil L Andersen of the Quorum of the Twelve taught us:
“We sometimes overly associate the power of the priesthood with men in the Church. The priesthood is the power and authority of God given for the salvation and blessing of all—men, women, and children.
A man may open the drapes so the warm sunlight comes into the room, but the man does not own the sun or the light or the warmth it brings. The blessings of the priesthood are infinitely greater than the one who is asked to administer the gift.”
He also said:
“All of the ordinances invite us to increase our faith in Jesus Christ and to make and keep covenants with God. As we keep these sacred covenants, we receive priesthood power and blessings.”
Please note, we all receive priesthood power and blessings. Men, women, children. All.
I recommend listening to Elder Andersen’s complete talk on Priesthood power.
Concerning your final question about faith and the success of blessings, please see my previous answer on this: Contradiction in Priesthood Blessings.