This is long, I will try to address the most obvious things.
1. Do these molar ratios look correct or realistic to achieve what I’m after?
Hard to tell without spending few hours calculating the exact equilibrium, but just skimming: look at the amounts of copper and citric acid in the first solution, there is no way to fully chelate copper with citric acid. Doesn't mean remaining copper won't be complexed by ammonia.
2. What is the correct classification for this reaction where you have neutralization occurring as well as chelation? Would it be an acid base neutralization? If so, it should produce a soluble salt (Copper Citrate & Manganese Citrate) and water correct?
It is not a single reaction, so there is no simple classification.
3. Is it possible to construct a balanced molecular or ionic equation for these?
For each reaction separately.
4. Citric Questions:
a. I understand this is a weak acid and can be expressed as H3C6H5O7 to represent that it can depronate one H+ from each of its carboxyl groups. I also understand each of these have a
different dissociation constant and can or will happen in a step wise fashion.
b. What do the dissociation constant values represent? Is it an amount of energy that is required? Is it only under certain conditions where each H+ will depronate such as pH value?
Please check the dissociation constant definition, I have no problems with explaining details once you get confused about something, but this subject is covered in every general chemistry textbook and I don't feel like writing one now.
Please look for equilibrium calculations, these are taught as either part of GenChem, Analytical or Physical chemistry. You have a system with several competing reactions, each of them has its own equilibrium constant, finding what is really happening in the solution can be challenging.