Everything from the 1 lessons of this topic on a few pages: the key idea of each lesson, the diagram to remember, the points to learn and the traps examiners set. Read it, cover it, test yourself.
Group 2 carbonates and nitrates become more thermally stable down the group. A small 2+ cation such as Mg2+ has a high charge density, so it has high polarising power: it distorts the electron cloud of the large CO32− or NO3− ion and weakens its C–O or N–O bonds, so less heat is needed to release CO2 or NO2. Larger cations polarise less. Solubility is linked to the enthalpy change of solution: ΔHsol = ΣΔHhyd − lattice energy. Down the group both the lattice energy and the hydration enthalpies become less exothermic, but at different rates. For sulfates the large anion means the lattice energy changes little while the cation hydration enthalpy falls a lot, so ΔHsol becomes less exothermic and solubility decreases. For hydroxides the small OH− means the lattice energy falls faster, so solubility increases.
Both terms get less exothermic down the group; the trend depends on which one falls faster, so never explain solubility with just one of them. Polarisation is about the cation distorting the anion, not the anion being attracted to the cation more strongly. And watch the sign in the cycle: with lattice energy defined as formation (exothermic), ΔHsol = ΣΔHhyd minus lattice energy, so −3080 − (−2833) = −247, not −5913.