I know that lambslove says yes to both, and that would be a good representation of the Arminian position (our member Mennonites are historically Arminian in position on the issue).
The historic S. Baptist position, as well as that of the Grace Brethren (other member groups here), OTOH, is that one cannot truly "come to know Christ, then by your own means let go of the salvation." We believe that a believer can step out of fellowship with God, and return to a life of willful sinning. However, since that person has been bought with a price, s/he is not his/her own, but belongs, is the possession, of Christ, and is also an adopted child of God, a member of the household. We therefore look at that person as the "prodigal son", the "lost sheep", the son in need of "discipline" from the Lord. And God has made clear through the NT writers that God will indeed discipline any child of his who is sinning willfully, so that they will repent and return to the light. If they keep on willfully sinning, he gives them a "terrifying expectation of judgment" -- not the judgment of condemnation with the world, but the judgment on believers, on the "household of God", for "judgment begins with the household of God."
Paul made it very clear to the Corinthians that if they do not examine themselves rightly, as to their conduct, God will judge them as believers, and that judgment can lead to sickness, and even death. Paul also told them that after death, one will appear before the "judgment seat of Christ", where their works will be judged, and they will give an account for their life. All the things they did that were not for God's glory will be "burned up." If they have nothing worthy to pass through that fire, they will "suffer loss" for eternity. Saved, but as "through fire."
God may seem to ignore the sins of the unbelievers, but believe me, he sees, and begins to work his discipline in the lives of his children, for their own good. You cannot lose your salvation, but if you fall away, and do not repent, you can expect God to find you, and give you a whipping. For you are his child. And God does not return his adopted children to the orphanage. And you cannot buy yourself back from the redemption. The price he paid for you was too great. You don't have enough sin. But watch out for the discipline. It is terrifying.
I should know.
Jeffrey A