Let's put the 'created equal' in context.

God said we were created equal. In his eyes, we are created equal (without sin) and you had no better chance of reaching heaven than I had on the day we were born. The example of a Down's syndrome child also has the exact same chance of accomplishing that.
You may be a better guitar player than me, but I may be better at building a house. Does this make one of us better than the other? No, just different. We all have gifts.

Level the playing field - We can all work on that at an individual level. If we do not judge on anything other than character (for lack of better word) then the field is level. If you want to judge by possessions you are doing it wrong. True joy rarely depends on possessions.

Redistribute Resources - are you talking about 'resources' or wealth? Resources are something that you can make something out of. They are pretty well available to all. It takes some creativity to see and develop the resources to have value.
Redistributing wealth is a whole different topic and defines capitalism versus socialism. We are learning that capitalism has a tendency to create 'entitlement' which is wrong. We are not 'entitled' to anything until it is agreed upon. This includes healthcare. If we in the US agree (in a majority at least) that we are entitled to it we will arrange for that. It is a discussion going on in millions of homes right now. The problem we have is one of numbers. We curently have a lot of older seniors who are leaving the work force and are 'entitled' to more than the system can currently provide, so adding more entitlements is a tough choice right now.
Another 'entitlement' we are battling is the false entitlement of greed. Large corporations are failing because of the greed of the corporate leaders. Yet our monetary system feels we need to bail out these failures in order to avoid the disasterous consequences of their failures. In a capitalistic society someone should step up to cover the needs of these failures. We the people did not cause the banks to fail, or GM for that matter. We enabled it but did not cause it, and yet we are paying for these failures. Yet another drain that is causing us to have to look very hard at the entitlements of others.

Again, in my eyes, if we do not accomplish these things (your three questions) individually we cannot expect the government to mandate it. It is obviously not the 'will of the people' if it is not practiced by them.

Also, I still think you are looking at equality as possessions and not the ultimate goal of how you live your life..
there *should* be compassion in doctors, there *should* be honesty in business, there *should* be a level field for all regardless of any defining physical characteristics. When we put those goals first, the rest will follow.
As it is, greed and 'me first' is the norm around the world. It makes progress that more difficult.

I have no problem with an individual wanting to earn millions, if done honestly. If I have to pay for your lifestyle it is not even. This leads to abuse. See welfare abuse for explanations.. it was created for the good of the people and has led to a stagnant existence for many. I am not trying to say welfare is bad, I have needed it a point in my life, and have no issue with supporting it, helping those with less. My issue is that I should not have to bail out those with more.
We all need to try harder, not to be rich, but to be better.

Make your sound your own!
.. I do not work here, but the benefits are still awesome