Regarding losing your salvation, the Church of the Nazarene believes that salvation is a gift that is provided by God through the sacrifice of Jesus Christ, but it must be freely accepted by a person. Just as the person has the freedom to accept that gift, he or she also has the freedom to abandon it if that person chooses. So, yes, the church does believe that you can lose your salvation.
Regarding the rapture, the Church of the Nazarene says little about end times other than that Jesus Christ will return in a Second Coming and that there will be a final judgement. There is no official statement about when the rapture will occur. Therefore, there are a variety of end times doctrines that exist within the church, including pre-, mid-, and post-Tribulation rapture beliefs, as well as premillenial, postmillenial, and amillenial beliefs that do not include a Tribulation at all.