Are we able to determine whether people are saved or lost upon their death?
We are in no position to assess someone's state of heart nor their destination upon death. A person may be a believer, who rebelled against the Lord in a severe and lasting way. If so, then that person was welcomed into the Lord's presence in the manner Paul describes in 1Corinthians 3:
If someone never accepted Christ as savior in a sincere way, and after a period of living as a cultural "Christian," they gave up the act and returned to their true nature. If so, then that person was demonstrating the truth that Peter taught:
In the first example, the Bible teaches that believers can - and do - stray from the Lord. In their disobedience, their life can resemble the life of an unbeliever. These children of God may even deny the Lord, much as Peter denied Christ during His trial. These denials are, in fact, lies just as Peter's denials were lies. Though it may be hard to accept, a true believer may claim to be otherwise, may sin in egregious ways and make every effort to distance themselves from Christ in this life.
But as Paul wrote:
In the second example, the Bible teaches that people can portray themselves as Christians in a convincing way, even to themselves. These portrayals include confessions of faith, the appearance of godly living, and even a degree of Biblical knowledge and piety. The Pharisees of Christ's day are the best example of this kind of counterfeit religious observance.
Nevertheless, such impostors were never truly born again as one of God's children. The missing ingredient was saving faith. The Bible says that saving faith is a gift of God, not something men acquire for themselves:
This is the "gift of salvation" you mentioned. Saving faith itself is a gift, and once it comes to a person, they confess and believe are are saved forever. The gift comes with the power of the Holy Spirit, Who indwells the person permanently as a down payment on the eternal inheritance God has granted to the believer:
Therefore, while we cannot say what happens to someone upon death, we can caution anyone from arriving at a doctrinal understanding through an analysis of any one person's life. Since unbelievers can act like believers and believers can act like unbelievers, we cannot rely on such observations to form conclusions about the truth of salvation.