Leander,
Since others have taken a try at answering your questions, I figured I'd try too.
If God really wants us to know him, why would it be so difficult for mankind to get a similar or correct understanding of his word the bible?
This, to me, kind of presumes mankind never has gotten a correct understanding of Scripture. Possibly no one person or group has succeeded 100%, but the basic teachings seem fairly broad. The Golden Rule, love for God, are blanket principles applicable in so many situations. If, for example, everyone was always honest and all the world had been since day one, would this be considered bad? So maybe the question becomes, if we practice Biblical principles that we know about wholeheartedly (iow once we know a principle we do our utmost to live it/apply it daily) that we see are good and logical, aren't we growing in knowledge of God?
Why would Satan be allowed to corrupt or alter God's word when there are honest people truly seeking to learn about God thru the bible?
Because sin came into the world because of his ambition and our arrogance. Instead of reconciling people to fit the Gospel, we do the reverse. Anytime a schism arises in a denomination over a doctrinal or other viewpoint an opportunity is created for the creation of yet another branch of Christianity. Many prefer the new to the old. And many times the "new" is less restrictive than the old. We want our standards, not His. Politics within a church can play a role too.
Why are there no miracles, prophets or divine influence in modern times the way it was in bible times? Especially considering that our time period is one that has the greatest need of any other period in human history?
Paul said such things would cease. The late Jeanne Dixon felt her prophetic abilities were a gift from God. But consider that when predicting President Kennedy's death, she took three times to get it right. And was it so hard to predict someone wanted to kill him? Anti-Castro Cubans blamed him for the failure of the 1961 Bay of Pigs invasion; the CIA hated him because he blamed it for the invasion's failure, wanted to "smash it into a thousand splinters and scatter them to the four winds of heaven," and planned a review of its worldwide activities; the Teamsters Union hated him for his not reining in his brother Bobby, who as Attorney General had exposed Mob influence in labor unions and who was daily battling with Teamsters President Jimmy Hoffa; the Mob hated him because they were getting rich by loans from the Teamster's Pension fund they never intended to repay, and their ability to keep doing that was hampered by Justice Dept. investigations; the Right hated him for appeasing Kruschev and abandoning Tito, as well as his civil rights initiatives; and Texas oilmen didn't like his efforts to repeal the oil depletion allowance as an income tax deduction. So Jeanne Dixon wasn't exactly going out on a limb.
Remember what was said in the parable of the rich man and Lazarus about sending the dead to tell the living of the fates awaiting them after death? The answer was made that if they didn't believe the prophet's warnings, someone from the dead wouldn't convince them either.
Miracles occur; we just don't recognize them. The sun shining for billions of years past and in the future; a flower blooming in the hostile desert; the planets maintaining precise orbits around the sun; an ant able to lift several times its own weight; larva to caterpillar to butterfly are some examples. We are the creators of everything unnatural, yet for all our technology we can't create a blade of grass.
If angels were persuaded to leave heaven and join in with Satan, why would God banish Satan and all his demons to the Earth where imperfect humans dwelled? If angels who lived in the very presence of God fell prey to Satan what hope is there for humans?
Satan was sent here to confine him and to send notice his time's about up--for his knowledge as well as ours. IOW, God has a timetable and the experiment of allowing us to do our own thing is about up.
What hope for us? Even sinners can do the right thing if left alone to do so. Every person who does right is living proof Satan wasn't right in his claim we only do good because of what good was done to us. And what of those who do good when there's nothing in it for them? They give to charity, mentor teenagers or ex-convicts, teach someone to read, and so on. There are temptations and there are chances to meet the needs of others.
Why have humans through-out bible history been punished with death, yet Satan and his demons have lived for thousands and thousands of years? Also has there been any human who has sinned against God the way Satan has?
I believe in the Society's explanation: when we rebelled in Eden we said to God that we'd make our own path. He's let us wallow in the muck of our efforts. We've accomplished many things, but what use are they if we can't end death or disease, crime, poverty, and so on? Anyone trying runs up against opposition from others benefitting from the status quo. If Satan doesn't rule us, how explain those who would steal food and medicine given to help others in order to sell them on the black market for their personal gain?
Satan's been allowed time to try and prove his claim about human motivations. Think what the knowledge of certain death would do to someone, and you aren't allowed to tell God you're sorry because you were once perfect like Adam and Eve. Wouldn't that drive you literally insane after a few hundred years? So you try and take as many with you as possible while trying to prove your point.
I'd say Adam and Eve qualify for your second question. Anyone else who's demanded worship from others, being accountable to no one, would qualify in my mind.
Just my $.02 worth.