Ah, an age old can of worms condensed into a post. Bear with me, I'm agnostic, but know enough about Christianity and respect it to try and answer.
Are good works simply byproduct of faith?
Good works do not seem to be such. Several species in the animal kingdom will do selfless acts like care for disabled (crows) and help fellow animals even if they put themselves at risk (a chimp rescued a drowning chimp out of selflessness). While we can't read their minds and see if they have faith or connection to God, we can at least see them as good with or without it. Another is men and women who do good even if they lost faith or never knew it in the first place. Love, compassion, and empathy run deep within humans - God gave us said gift even without faith as he loves even the nonbelievers, and hopes our compassion drives us to the community of the church.
How can we possibly claim to believe in salvation by faith-alone if we affirm that even faith, without works is dead? How can we uphold the Sacrament of Baptism, Absolution, Eucharist as the means in which God distributes his grace and still claim to adhere to Sola Fide?
You know you struck a great question when
entire schisms happen within Christianity over it. I'm going to take this out of the theology realm and into the origins of religion area.
So, when you start a religion, you're basically implementing a set of laws and guidelines for people to follow. It's a great way to get unruly or selfish people (attention whores who do good deeds for the wrong reasons are still being lawful) to do good for a community. However, it can be read as a currency to get into heaven, which isn't what it is meant to do: donating to charity and volunteering does not grant one the right to fuck your neighbor's wife even if you think you redeemed enough goodboy points to do so. Some abused it like a couponing system, so it's logical that another branch would rebel against it.
Granting people salvation based on faith alone is a better way to get people to actually commit themselves to the church and take that shit seriously. It places more empahsis on learning church practices and the theological thought process. It gives more leniency towards those who sinned and believed themselves irredeemable: you may stray from the path but you can always come back. It's comfort and forgiveness.
...it also is a great way to get people to come to your church. Don't feel like doing shit? Just have faith and you're good! It is slightly more accepting and lazier than the previous method. It too can be abused: what is the point of following a teaching if I am forgiven for whatever I do?
Ultimately, I think it comes down to how you view it. I like option A better, as God prefers committed followers, even if they stray from the path. He forgives, and wants people to try again by being good.
And how can they claim that they will lose God's grace because of sin, even though it is said in Psalm 14, Romans 3:10 that nobody is righteous?
Personal guilt is a bitch. So is grudges and hatred for others who commit things like senseless murder. We may have the capacity for love, but we also have the capacity for violence and hatred too.
It can be used by the church to manipulate people as well: ya dammend if you do or don't do this. What a churchman says and what the Bible or your gut say are different things.