1) Magnesium and chlorine form an ionic bond. Covalent bonds are formed when two or more atoms share electrons between them. Ionic bonds are when atoms gain or lose electrons to become charged species (ions) that share an electrostatic interaction called an ionic bond. Magnesium forms a positive ion (cation) with a 2+ charge and chlorine forms a negative ion (anion) with a 1- charge. So two chlorine anions form an ionic bond with one magnesium cation for form MgCl2, a neutral chemical compound. Metals and non-metals often form ionic bonds because of the difference in their electronegativity values. Electronegativity is basically a measure of how strongly an element will attract electrons toward it. Chlorine (a non-metal) has an electronegativity value of 3.0 and magnesium (a metal) has an electronegativity value of 1.3. This makes a difference of 3.0 - 1.3 = 1.7. In general, any electronegativity difference of 1.6 or more is considered an ionic bond, and MgCl2 falls into this category.
2) The general rule of thumb about solubility is that "like dissolves like." In other words, polar solids tend to dissolve in polar solvents and non-polar compounds tend to dissolve in non-polar solvents. We know that MgCl2 is an ionic solid, so we know that it is a polar compound since it is made up of ions. Water (H2O) is a polar solvent. The electronegativity difference between hydrogen and oxygen is about 1.4. This makes water a polar covalent molecule where it still has covalent bonds but there are partial charges on the atoms, hence the polar nature of water. MgCl2 dissolves in water because the individual ions in the solid (Mg2+ and Cl-) coordinate with the partial charges in the water molecules. The magnesium cations coordinate with the partially negatively charged oxygen atoms and the chlorine anions coordinate with the partially positively charged hydrogen atoms. Since numerous water molecules can surround each ion and separate them, this causes them to solvate, or dissolve in the solvent.
3) There are two basic kind of mixtures, homogeneous and heterogeneous. Heterogeneous mixtures are composed of two distinct phases, like sand in water. Homogeneous mixtures are composed of a single phase. Seawater is an example of a homogeneous mixture. The MgCl2 and other ionic solids are completely dissolved in the water, thus forming a single phase to the eye (liquid water). In fact, all ionic solutions are considered homogeneous mixtures.