Yes
The underlying concept of evolution is essentially that genetic variation gives a spread of traits around the normal (think a Bell Curve), and filtering that spread (via natural or artificial selection) so that more organisms towards one end of the Bell Curve reproduce than the other end, so that the next generation has its normal shifted toward that end. Then lather, rinse, repeat until the normal has shifted so far as to qualify as a new trait.
This entire process was experimentally demonstrated by Lenski's E. coli experiment - https://myxo.css.msu.edu/ecoli/
Don't think this is the only example though, there are literally thousands of examples of evolution being directly observed to occur.
Did you know corn does not exist in nature, but instead was created by man through artificially guided evolution?
Evolution is an observed fact, every bit the fact that gravity is. The Theory of Evolution only refers to how we think evolution works. It has nothing to do with whether it happens or not, we know it happens without a doubt. Likewise, we have the Theory of Gravity to explain how gravity works. If the Theory of Gravity is wrong, it's won't change the fact that rocks fall to the ground, it would only mean we don't understand why rocks fall. If the Theory of Evolution is wrong, it won't change the fact that animals (including us) evolve, it would only mean we don't understand why they evolve.
See here:
http://www.talkorigins.org/faqs/evolution-fact.html
And for the Theory of Common Descent by evolution (which has nothing to do with the fact that evolution occurs OR how evolution occurs, but shows the evidence that makes us think all life evolved from a common ancestor) see these:
http://www.talkorigins.org/faqs/comdesc/
http://www.talkorigins.org/faqs/homs/
And use the search button of TalkOrigins for any questions you have, it's a great resource.
edit: I gave you examples, did you even read my damn post? Jeez, trying to reason with a godbotter is a waste of time...
"Cosmic Evolution-the origin of time space and matter from the big bang. Big bang-infinitesimal region that spun around really fast and then broke apart."
I have no idea what you're talking about. No where in the big bang theory does it say anything about a 'infinitesimal region that spun around and broke apart' nor does it say anything about 'the origin of time space and matter'. The only context in which the words 'cosmic evolution' make sense is discussing the evolution of galactic structure. Look up 'Hubble Ultra Deep Field'
"Chemical Evolution-the origin of more complex elements that came from the hydrogen produced by the big bang."
Easy as pie. Look at any nuclear reactor. That's what they do on a daily basis, take one element and form another from it. They do fission reactions - forming lighter elements from heavier ones. If you'd rather see a fusion reaction - forming a heavier element from lighter elements like hydrogen (what you're referring to), look at a particle accelerator, that's what THEY do.
Or, you know, look at that big bright yellow thing in the sky. It's a giant fusion reactor that forms elements up to carbon from hydrogen. They call it the sun. Fuses millions of tons of heavier elements from hydrogen every day, right in front of your eyes. Really! Go out and look, I'll wait!
Did you go look?
Anything heavier than carbon gets fused in supernova explosions, which also serve the purpose of spreading the newly fused heavy elements out to form new stars and systems.
"Stellar and Planetary Evolution- the origin of stars and planets form dust clouds"
It's been directly observed, as well as modeled. See an HR Diagram - http://www.ifa.hawaii.edu/~barnes/ast110_06/tlos/HRDiagram.png
"Organic Evolution-life from non-living things"
First, define life.
When you see how futile that is, then try to get your head around the idea of a continuum where life and non-life and meaningless arbitrary terms. Then look up the Miller-Urey experiment. THEN, if you're REALLY feeling up to the task, search for 'RNA World'.
"Macroevolution-one kind animal changes into another like an ameba slowly becoming an elephant"
I gave you all the relevant links originally. Lenski's experiment proves novel, beneficial traits can be acquired through mutation + selection. The TalkOrigins links give you tons of evidence.
You didn't even look at them, did you? You just decided you must be right and you're happy to stay in ignorance than try and actually learn something.
Besides, NONE of these 5 things you just asked about have ANYTHING to do with your original question, which was to prove evolution, meaning the process, which in itself does not include common descent, abiogenesis, or cosmology.