Q1) What makes a particular interpretation of such-and-such a passage convincing to you?
It needs to square with the overall portrait of God given in scripture, which is ultimately that God is love, light, a consuming fire, salvation, spirit, One. That God is just, merciful, faithful, the Father of all, mighty to save, and so on. Also that God is loving toward all (as in 1 Cor 13) and that nothing He decides to do can be denied Him.
It needs to make sense logically – that is, it cannot contradict itself, nor can it contradict the other opinions which the person offering the interpretation has also espoused. If it seems to contradict other scriptural passages, I’ll need an explanation for this apparent contradiction.
Q2) Why do you think other people are not convinced by the same things you are?
People have varying reasons for this. Some honestly look at all the evidence and see things differently. Some have a higher opinion of the traditional positions of the church than I do. Some haven’t seen all the evidence, and are so persuaded by what they already believe they know, that they aren’t able to look at all the evidence objectively (yet). People give varying weight to different types of evidence. Often people take passages literally that were (imo) intended to be taken metaphorically, symbolically, mythically, etc. People hold differing opinions on what it would or would not be moral and right for God to do. Many people truly cannot see that they themselves practice selective interpretational methods – ie, they interpret the same passages in opposing ways, depending on how they wish to use the passages. And no doubt there are many more reasons besides these.
Q3) Is there any way to resolve differences of interpretation between people?
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It depends on the people and on the strength of their opinions – also on the particular scriptures themselves. Some scriptures genuinely do contradict one another. For example, in the Pentateuch we see (apparently) God commanding Moses concerning sacrifices and offerings. Yet later in the prophets (Isaiah I think?) God says, I gave you no command concerning sacrifices and offerings. Here, I think, is a reason to consider that the bible may be a collection of literature BY human beings ABOUT God and, while inspired and profitable for many things, not always laying out the entire, or entirely accurate portrait of God. This is why we need to take scripture in the context of the entirety of scripture – and in context with the revealed nature of God in Christ Jesus.
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Q4) Given that many more educated people than you disagree with your interpretation, how confident can you be in your opinion?
Education and study, cultural, linguistic, literary knowledge and analysis are vital tools for the interpretation of scripture – however – these things must not be expected to LEAD to life. The life of the community is important, and I think this life/knowledge of God, is often subjugated to the opinions of highly learned men which are imposed from the top down. People submit to these rulings because they are told they must, since said highly learned men explain to them that they (the learned) are placed over them (the commoners) by God, for the good of their souls. Perhaps this is accurate, but history and current events have shown alike that such is not always an accurate claim.
I think that we must use the tools that God has given us (our brains), but that the brain/intellect must always BE the tool of our spirits/hearts which ought always to be listening to God’s Holy Spirit at that deepest level of our being (that is, the heart/spirit). We must live from our spirits/God’s Spirit, and the brain be subjected to the heart/spirit. If we live from the intellect, we will always disagree. I think that it is eventually possible, for those who drink of the Spirit liberally and consistently, to agree.
Q5) What are the ramifications of this?
We always choose to eat from the wrong tree when left to ourselves. Jesus came to give us life. (He is the Tree of Life, I believe.) But we want knowledge. We worship it in fact, in western society at least. Knowledge is a good thing, but a servant who usurps the authority of his master is a bad thing, and knowledge is meant to be the servant of spirit – not the other way round.
So . . . my opinion fwiw. 
