I prefer the NASB version:
John 15:1-3
1 "I am the true vine, and My Father is the vinedresser.
2 "Every branch in Me that does not bear fruit, He takes away; and every branch that bears fruit, He prunes it so that it may bear more fruit.
3 "You are already clean because of the word which I have spoken to you.
So, what does "takes away" mean? Are we justified in thinking it means "ejected from God's family"? "Airo" in the Greek means "to hoist," or "lift up," or "to bear." It may also mean "take away" but given the practices of ancient Jewish vinedressers, it is very unlikely this would have been the way Christ's words would have been understood. According to Pliny, in Jewish viticulture, spring pruning did not involve the removal of all non-fruit bearing branches but mainly suckers on the sides of fruit-bearing branches. Non-fruit-bearing branches were vital to the maintenance of healthy vines in the next growing season and so were lifted up onto trellises to avoid moisture damage. (see "VITICULTURE AND JOHN 15:1-6" by Gary W. Derickson. Gary W. Derickson is Associate Professor of Biblical Studies, Western Baptist College, Salem, Oregon. This author holds B.S. and M.S. degrees in horticulture from Texas A&M University and taught grape-pruning as a teaching assistant there. )
Or, better:
John 15:6
6 "If anyone does not abide in Me, he is thrown away as a branch and dries up; and they gather them, and cast them into the fire and they are burned.
Compare this verse to the following passage:
Ezekiel 15:1-5
1 Then the word of the Lord came to me, saying,
2 "Son of man, how is the wood of the vine better than any wood of a branch which is among the trees of the forest?
3 "Can wood be taken from it to make anything, or can men take a peg from it on which to hang any vessel?
4 "If it has been put into the fire for fuel, and the fire has consumed both of its ends and its middle part has been charred, is it then useful for anything?
5 "Behold, while it is intact, it is not made into anything. How much less, when the fire has consumed it and it is charred, can it still be made into anything!
Both the verse in John 15 and this passage in Ezekiel 15 emphasize the same thing: uselessness (as opposed to destruction). Rather than seeing John 15:6 as teaching a saved and lost doctrine, it is better understood as describing the spiritual uselessness of those who, though adopted into God's family, do not abide in Christ their Saviour as a constant, moment-by-moment state of affairs.
Romans 11:17-23
17 But if some of the branches were broken off, and you, being a wild olive, were grafted in among them and became partaker with them of the rich root of the olive tree,
18 do not be arrogant toward the branches; but if you are arrogant, remember that it is not you who supports the root, but the root supports you.
19 You will say then, "Branches were broken off so that I might be grafted in."
20 Quite right, they were broken off for their unbelief, but you stand by your faith. Do not be conceited, but fear;
21 for if God did not spare the natural branches, He will not spare you, either.
22 Behold then the kindness and severity of God; to those who fell, severity, but to you, God's kindness, if you continue in His kindness; otherwise you also will be cut off.
23 And they also, if they do not continue in their unbelief, will be grafted in, for God is able to graft them in again.
This passage addresses Jews and Gentiles as groups of people and states simply that unbelief toward God in either group will result in the same separation from Him. The Gentiles, then, were not to think of themselves as superior to the Jew but as much a recipient of God's kindness and as much dependent upon Him as any of His Chosen People (however alienated from God they may be). The passage does not teach a saved and lost doctrine but is, instead, an injunction to Gentiles to maintain reverent humility and belief toward God for one cannot have a relationship with Him apart from these things.
Not so. In the parable of John 15 the branches are not cut off but lifted up (vs. 2) and/or may become useless to God (though not un-adopted - vs. 6). The passage in Romans 11 is a reminder that, whether Jew or Gentile, without humility and faith toward God one cannot have a relationship with Him.
Yes, I still firmly believe that once one is saved, one is forever saved. Other passages and verses qualify the ones you've offered in such a way as to make a saved-and-lost perspective impossible.
1 Thessalonians 5:23-24
23 Now may the God of peace Himself sanctify you completely; and may your whole spirit, soul, and body be preserved blameless at the coming of our Lord Jesus Christ.
24 He who calls you is faithful, who also will do it.
Philippians 1:6
6 being confident of this very thing, that He who has begun a good work in you will complete it until the day of Jesus Christ;
Hebrews 13:5
5 Let your conduct be without covetousness; be content with such things as you have. For He Himself has said, "I will never leave you nor forsake you."
John 10:29
29 "My Father, who has given them to Me, is greater than all; and no one is able to snatch them out of the Father's hand.
Selah.