I think some of that was in fact the institutions of man--slavery, stoning, and so on...it's very telling that Jesus sows the seeds for these things to stop, during His ministry. There are some who are guilty of selective reading to perpetuate these things (think some of the Confederates, for instance), yet there is no way to read how Jesus calls us to conduct ourselves towards others and think that slavery in any way squares up with those teachings. The cultural revolution against slavery became inevitable.
It is quite interesting that at a couple points, the Bible does directly address the fact that the institutions of man are not right, not what they should be. God's reaction, for instance, to being asked by the Israelites for a king is very telling--He very directly calls the Israelites out on the fact that this is an institution of man and one that has been tremendous trouble for neighboring nations, and that if they keep insisting on doing this with or without His blessing, it will just lead to corruption and heartache. (Which it did...aside from certain bright spots, Kings and Chronicles outline a very turbulent and troubled period for Israel and Judah with a lot of political conniving and bloodshed that ends in subjugation and exile.)
When the people of Israel turn out to be unrelenting, set on their course regardless of this counsel, God respects their free will and anoints a king. He does end up using this to do something good in the far future (Jesus is stated to be of David's lineage), but it's made very clear that other than this, the institution of a kingdom was NOT a good or desired thing. There are some other instances along these lines, but this is where God most directly takes on the subject, that we have recorded, of exactly how people get this habit of folding THEIR created institutions into religion. He calls it exactly what it is and expresses staunch disapproval. To my mind, this is quite the striking moment of honesty and one that makes me stand up and take notice. (I do not imply dishonesty at other times, but given that sometimes God presents Himself in a very understated and cryptic way, something this blunt is VERY attention-getting.)
As to the free-will issue...that goes back to something I said earlier, that for God to abrogate the free will of an individual or set of individuals is, according to the evidence, the greatest atrocity possible, beyond physical death by several orders of magnitude. Destruction of the spirit and mind ranks WAY beyond the destruction of the body, and this goes a long way towards explaining the attempts to counsel humanity that the course they're taking is wrong, but subsequently backing off when people are dead set on choosing otherwise even though the results are not going to be good.
Your first and second examples very much fall into this category: something that was NOT right that people went and decided to fold into their religious practice. They should NOT have done it, and went and did it anyway and were not going to be turned away from it until much later in human history when people finally sat up and PAID ATTENTION to what God had been telling them all along. As to the laws that deal with slavery, stoning, and so on--some, I believe, were attempts to soften the blow (Jubilee, for instance, should've freed slaves every seven years. Note, however, that the custom was NEVER practiced and we ended up with perpetual servitude instead.), make people question themselves and listen to their conscience before it got to that point (putting obstacles in the way before a punishment came to pass)...and others, quite frankly, were indeed people mixing their politics in with their theology. And this was flat wrong.
The fourth contention, that we are not invited to look at or examine evidence...this one I do not believe stands. Ultimately, a decision must be made based on a best estimate, and this is the decision of faith. This is what is meant when it is said that we should "lean not on our own understanding": we can investigate as much as we can...and we should, but ultimately our minds do not contain everything, and that final decision is in effect a leap. That does NOT, however, mean that we should not strive to understand as best as we can. God Himself says as much when He states that Solomon, in requesting wisdom as his reward, has made the most worthy decision possible.
As to how I practice this in my own life and belief, I spend much time investigating and considering the logic of my belief, and I also spend a great deal of time considering other aspects of knowledge, too, to include the natural sciences. I have no fear of things like evolution, the Big Bang, string theory, or any other thing science could accomplish or reveal...I won't shy away, because I believe that we SHOULD strive to understand as much as we can about the world we live in just as we should strive to understand who we are and what our purpose is.
Your third point is the most difficult one, because there seem to be multiple explanations in each case. Some cases appear to be of an almost accidental nature and these are quite simple to explain: for instance, dying as a result of touching the Ark of the Covenant or looking directly upon the presence of God. While you may not accept this, it is my belief that such deaths occurred because the human body and nervous system simply could not handle the massive input this sort of contact brought on, and the result was instant death. Warning people not to do these things is no different than warning your child not to stick his fingers into an electrical socket--your child doesn't do it out of malice, and electricity isn't evil, but there is a natural cause and effect with electricity: if you're not grounded, you're very likely to be seriously injured or killed.
There are other deaths that might have been mercy killings--some deaths may have occurred when they did to prevent someone from being too far gone in the eternal sense. We're not always told what happens to the souls of those who in the Bible are struck down--what happens in the moment between life and death is not something that we know. Personally--and this is just gut instinct, mind you--I think it is possible the moment of death is a moment of final choice.
However, this idea necessitates extreme caution. It's very, very easy to go from this to the idea that we can just kill people willy-nilly and claim it's for their own good. And some HAVE gone there, and they were dead wrong. Which leads perfectly into my last point...
There are absolutely cases where people use their beliefs to justify whatever atrocities they have in mind, and some of those incidents are on the historical record. Some of them are likely on record in the Bible, which serves a dual purpose as theological guide (what OUGHT to happen) AND historical record (recording what really happened, some of which very much was NOT right). This is true in the modern era and it was true in the past as well. Those who commit such acts "in the name of God" commit a blasphemy of actions as well as words and they are absolutely responsible for what they've done. These are not acts of God, but the acts of those who smeared His name as though He endorsed their hate. These incidents seem pretty frequent, at least to my own gut reaction--though lacking the knowledge of the eternal fates of those involved, I can't actually name percentages.
Edited to add: I see that Silvercrest has addressed this third category in much more detail and I commend his explanation, which is much better worded than my own. He also addresses the ramifications of the Bible being dual theological treatises and historical record quite nicely, too. (Incidentally, the NT does show this as well, particuarly in the letters of Paul, where some of Paul's comments to specific people and individuals have been bent WAY out of context.)
Again, this is just my personal take, and some of it is very much gut instinct. Your third question is one to which I continue to direct much study because I recognize its enormity. What you have now is an early answer and not yet as complete as I would like it to be.
Anyway...I've got to go to work shortly and given the speed at which this thread is moving, I am not likely to be able to address very many, if any, of the posts that occur in the next 8 or 9 hours or so, perhaps not even until tomorrow. I have, however, enjoyed the thought-provoking discussion and hope to pick up at a later point.