[Organishe]

The second equation looks fine to me. For the first one, it's kind of arbitrary to write an equation like that.  At the level you've gotten into chemistry you probably haven't been introduced to net ionic equations, so here you go    Net ionic equations show only the species that undergo state changes or are created or destroyed.  So, going to the first equation, all 4 of the compounds you've shown will be highly soluble in water, so everything dissociates and is happy being in solution.  Therefore, adding copper sulfate to hydrochloric acid has no net effect.  The catch here is that the HSO₄^- ion is not a "strong acid", so it will not completely dissociate, and this could alter things a bit.


Perhaps this will better illustrate what I'm trying to say (I don't think i'm doing so hot so far)

Also, let's assume sulfuric acid is a "strong" diprotic acid (both protons completely dissociate) and the same for HCl (only 1 proton)
Reactants:
Cu²⁺  + SO₄^2-+ 2 H⁺ + 2 Cl^-

Products:
Cu²⁺  + 2 Cl^- + 2 H⁺  + SO₄^2-


Every single ionic species we start off with, we end up with the same exact thing in the end.  Although in our equation we wrote them as if certain ions are bonded to other ions, in actuallity everything is just floating around, so we can't really say what is with what.

A link for your enjoyment 

http://www.towson.edu/~ladon/netionic.html

As to your question about "what happens when sulfates and carbonates mix", the production of carbon dioxide is a property of the carbonate ion.  Adding an acid to carbonate salts causes them to gain protons, thus creating H₂CO₃ (carbonic acid), which then rapidly decomposes into water and carbon dioxide.

[P-man]

Aha, that makes it clearer. So the H₂SO₄ would become a muddle of ions in a solution. What would the ionic equation look like?

[xiankai]

since H₂SO₄ undergoes (near) complete dissociation, what does it contain in the first place? no chemical reactions, but just seperation of its original ions

[P-man]

So we have a muddle of ions in a solution... very exciting! Well now this is all cleared up. No more wondering, thanks to you guyses. Time to fulfill the first equation...