Thank you for your interest in the issue of Eternal Security. Simply stated, when it is understood that we are saved by the grace of God, not on the basis of our personal merit, these matters are far more understandable. The passages that you cited, in 1 Corinthians & 2 Peter, we see the difference between those who "profess" Christ as opposed to those who actually "confess" Christ. For instance, 2 Peter 2:20 describes those "False Teachers" who were professing themselves to be followers of Christ having escaped the defilements of the world, but then rejected what they professed, becoming slaves of corruption (v. 19) and showing their true, natural unchanged condition (v. 22).
The issue rests on the competency of our God to keep His Word when he states that "All that the Father gives Me shall come to Me, and the one who comes to Me I will certainly not cast out." (John 6:33). The most important factor is not whether one professes to be a believer, but whether they ACTUALLY ARE a believer. There are those who profess, and yet will be denied by Christ on judgment - cp. Matthew 7:20 ff. The important factor is whether one has a personal relationship with Christ Jesus that makes a daily difference in the way a person lives.
Whereas Eternal Security is an issue dealing with the work of God, the issue of Assurance is how we feel about our salvation. Eternal Security is not dependent on any circumstances. The lack of one's Assurance of salvation is often dependent on the issue of indulgence in sin. The difference is important to recognize.
Hopefully, these comments have been helpful. If further consultation would be helpful, do not hesitate to let me know.