Yes, I have in fact studied the Bible through looking for what it has to say on the subject. I don't rely on just one verse to back me up, I simply use it here primarily because it is probably the clearest and least refutable passage concerning falling away.
You may wonder how I can reconcile MY beliefs with the passages you brought up. Glad you asked.
John 15 - I agree.
"He doesn't say he used to know them and then they were lost, he says he never knew them."
He says MANY will say to me in that day. Just because there are a bunch of people who never were saved trying to convince Jesus that they were does not mean that there will be no people who actually were saved and now are not. In Hebrews 6:4-6, Paul actually describes some who already did fall away.
1 John 2:19 "They went out from us, but they were not of us; for if they had been of us, they would have continued with us; but they went out that they might be made manifest, that none of them were of us."
Upon closer examination, the meaning of this verse becomes clear. What is the meaning of the word "manifest?" It of course means to make plain or visible. People departing from Christ is not visually recognizable, but people leaving the body of Christ is. So these went out from among the body of Christ that it might be manifest that they were never truly a part of it. This does not imply that one who truly is a part of Christ's body cannot turn away from Him and be lost.
You wrote: Jesus promises he will never leave us or forsake us.
But recall that God's promises are conditional. Consider those to whom He originally spoke those words:
Deuteronomy 4:31 "For the LORD thy God is a merciful God; he will not forsake thee, neither destroy thee, nor forget the covenant of thy fathers which he sware unto them."
But He also said,
Deu 31:16-17 "And the LORD said unto Moses, Behold, thou shalt sleep with thy fathers; and this people will rise up, and go a whoring after the gods of the strangers of the land, whither they go to be among them, and will forsake me, and break my covenant which I have made with them. Then my anger shall be kindled against them in that day, and I will forsake them, and I will hide my face from them, and they shall be devoured, and many evils and troubles shall befall them; so that they will say in that day, Are not these evils come upon us, because our God is not among us?"
So God's promise not to leave or forsake us is conditional, for He certainly will forsake us if we forsake Him. As 2 Chronicles 15:2 puts it,
"And he went out to meet Asa, and said unto him, Hear ye me, Asa, and all Judah and Benjamin; The LORD is with you, while ye be with him; and if ye seek him, he will be found of you; but if ye forsake him, he will forsake you."
You wrote: "He has the power to keep us safe to the end."
I agree. But I believe that we must continue to abide in Christ for Him to keep us. The scripture says that we are kept by the power of God through faith (1 Peter 1:5), but that faith can be made "shipwreck" (1 Timothy 1:19).
John 14:16, yes the Spirit was given to the followers of Christ to abide with them forever. But this promise is also conditional. Remember King Saul, who grieved God so much that the Holy Spirit departed from him (1 Samuel 16:14).
You wrote: "What kind of Savior can you offer people if He is unable to keep you till the end?"
While I do believe that our power to stand comes from Christ, I also believe that man also has a responsibility in accepting Christ and abiding in Him, I see no scripture to the contrary.
God wrote: Isaiah 49:15 "Can a woman forget her nursing child, And not have compassion on the son of her womb? Surely they may forget, Yet I will not forget you. 49:16 See, I have inscribed you on the palms of My hands; Your walls are continually before Me.
But He also wrote: "As I live, saith the LORD, though Coniah the son of Jehoiakim king of Judah were the signet upon my right hand, yet would I pluck thee thence." (Jeremiah 22:24)
I am very happy to hear about the woman you mentioned. My wife's great-grandmother was much the same way (except that she had been a Christian her whole life). Good questions though. I hope that even if you don't agree with me, you can at least understand why I believe the way I do.