Dissociation reactions and Ksp values

Hi all. I was just wondering how to write balanced dissociation equations (and how to determine the charge of things/the charge of compounds).

For example, in class we were given a compound. It was CaCO3 (calcium carbonate). According to the answers, the products of the equilibrium reaction are Ca²⁺ + CO₃^-. My first question: How do we know what the products are going to be? (i.e. how do you know that the products aren't going to be Ca + C + O instead?). My second question: How do you know what charges the chemicals are going to have? I always assumed you could just use the periodic table, but our teacher said you can't for transition metals (why is that?). My third question: how do you know what type of reaction is going to take place, without being told? For example, how do you know the above reaction is going to be a dissociation reaction, without someone telling you?

Also, I was wondering if someone could very simply explain K_sp values to me. I've looked on the internet, but I still don't really understand. As an example, would someone be able to solve the following problems:

1. Calculate the concentration of silver and chloride ions in a saturated silver(I) chloride solution at 25 degrees Celsius. K_sp(silver(I)chloride) = 1.8 x 10^-10

2. Calcium fluoride has a K_sp of 3.9 x 10^-11 at 25 degrees Celsius. Calculate the concentration of fluoride ions in a saturated solution at equilibrium

Thank you so much! Hope everything makes sense! 

🙃