When I say intelligent design, that does not nessessarily mean "God".
For all we know, our whole universe is inside a test tube in some laboratory.
Also conceivable, as is that we might be somehow created by aliens. I just don't see much in the way of evidence for those hypothesis.
What raises questions for me is where the balance comes in. Trees make oxigen and we exhale carbon dioxide. Stuff like that.
In a quantitative sense, the balance is self-correcting. If you mean however how the situation established itself in the first place, with a certain kind of need being matched by those of other beings, then it seems to me that it is indeed a matter of luck of the draw. Certain patterns simply happened to thrive in the environment that they found out to some degree or another, and those more properly sustained lasted better and longer.
It makes sense to me that slow Lions and gazelles DNA did not reproduce. Thus the balance was established.
A dynamic sort of balance, yes. Several factors may upset it and force it into newer, now more stable patterns. For instance, often enough the population of gazelles and comparable prey will diminish to the point that lions and other predators will starve. That leads to auto-correcting by way of diminishing populations of predators, but sometimes alternate strategies may prove promising, leading to (say) more efficient use of eaten food instead.
You also raise the question that when we don't allow single mothers and their children to starve are we allowing our species to evolve into weaklings?
No, not at all! What I meant is that if there is an Intelligent Creator, he does not seem to have made a point of making humans particularly fit to healthy survival. There are way too many "design flaws", including those that make single mothers so darned easy an occurrence.
What would happen if slow gazelles and lions reproduced?
They do, just not as often and succesfully as faster ones. In every generation there is some variation in speed for individuals.
Natural selection will usually favor the faster ones, but there are always exceptions, and a sufficiently strong change in the environment may well make speed less of an advantage or even a disadvantage.
For instance, let's guess what happens if a third species is introduced, one that has an even more intense metabolism than lions and is therefore faster and more powerful than either lions or gazelles, but also more dependent on frequent meals (it hungers faster, perhaps as a consequence of his speed). Say that it also has very poor senses except for fast moving targets (many lizards do). If I am guessing the results correctly, it might weed out the fast lions and gazelles fairly quickly, while the slower ones would perhaps survive and be favored in the next generations of both lions and gazelles.
Nature is cruel for sure, but survival of the fittest did improve the species.
I don't think that is quite clear. What is meant by improvement here?
Natural selection and survival of the fittest sure did a lot to build a wild variety of species. If that is an improvement, than certainly there was much improvement. But I find that a bit of a misuse of the word, personally. Improvement in relation to what?
While it is humanitarian to allow our weak to reproduce, will we be reversing nature and will there be consequences?
Everything has consequences, including inaction.
The question you are asking here is essentially whether we will favor physical self-reliance over humanitarian and social responsibility.
And my answer is an emphatic no. Nature is rather unwise, literally mindless even, and it is our responsibility to assist it, in this case by keeping our population levels manageable (although it may be way too late for that), addressing our social issues, and taking responsibility for our present and future.
Far as natural selection goes, it never even had the capability for improving humanity in any meaningful sense. All it could and can ever do is improve our odds of surviving in some form and reproducing in order to ensure a further generation. We have far since reached the point where that is Just Not Enough.