1) Also from St. Paul: "though I have all faith, so that I could remove mountains, and have not charity, I am nothing." So, yes, it is possible to have a dead or lifeless faith that does not avail for salvation.
2) Logically, if we were saved by "faith alone," then our actions would actually not be of any importance at all, either way. Fortunately, most of us seem to have far to much common sense to buy that and do think that faith should lead to good works and a transformed life. Then again, that was and is the Catholic position, against which Luther and Calvin rebelled.
3) "If one is not seriously repentant, how can one be a true believer?" Do we not read that even the just man falls seven times seven times a day?