For many people, the gospel has strings attached: you can be saved by grace, but after that you have to work really hard. But the true gospel is that Christ died for all sins: past, present, and future. Does this mean that you can sin all you want? Yes. You always have, and always will. But God wants to save you from your sins, and he is really good at what he does - for you and for everyone else.
Are Christians required to keep the seventh-day Sabbath? No. Mike Feazell explains that the Sabbath was a temporary law, designed (like various other old covenant laws) to point to Christ. Now that he has come, we do not need the pointer when we have the real thing. Just as the old covenant days reminded the Israelites of their salvation from Egypt, new covenant worship reminds us of Christ.