1.) In the first place, this molecule doesn't exist under normal circumstances. On the periodic table, Aluminum (Al) has a charge of +3, while the polyatomic anion hydroxide (OH) has a charge of -1. If you remember the rules of forming ionic compounds, to figure out the number of atoms per molecule, just swap the superscript of one ion (the charge) with the subscript of the other. For example, Al, with a superscript (charge) of +3 becomes the subscript (or number of atoms) for OH, and vice versa. So the actual molecule for the compound Aluminum Hydroxide is Al(OH)₃. As I've already said, this is an ionic, not a covalent compound, because it is formed by the bonding of a cation and an anion. In general, molecules are ionic if they are formed by the bonding of a metal and a nonmetal on the periodic table, and they are covalent if they are formed by the bonding of multiple nonmetals together (for example, C₄, O₂, etc.).
2.) This answer is also false. Remember that molecules have two different kinds of geometries: an electron geometry and a molecular geometry. The electron geometry of PF₃ is in fact tetrahedral. But the electron geometry does not determine the "shape" of the molecule. The "shape" is determined by the molecular geometry, so we need to think about what the electrons are doing here. The basic Lewis structure should look something like this:
. . P F
This link will give you a better picture of the molecule. Go to page 374.
I cannot make a very accurate picture in a word document. But the basic idea is that P is covalently bound to three F atoms, with one remaining lone pair of electrons.
You can see the rough outline of what PF₃ looks like. The electron geometry (again, not the shape) is tetrahedral in the sense that the P atom is surrounded by three F atoms and one lone pair of electrons. But the shape (molecular geometry) is determined only by the positions of the atoms and is not directly related to the non-bonding electron pairs. But these electrons are very important in determining the shape. In this arrangement, the F atoms will not be able to remain equidistant from one another, because the lone pair electrons of the P are actually closer to the F atoms than they would be if they were bonded to another F atom. In other words, the repulsion of like charges (the lone-pair electrons on P and the lone-pair electrons on each of the F atoms, which you can see in the link I've provided) push away from each other. The effect will be to push the F atoms downward, with the P atom standing at their head. The resulting shape is kind of like a spider's body. This arrangement of atoms is actually called "trigonal pyramidal" because three atoms (trigonal) form a pyramid-like molecular shape (pyramidal). Therefore, the answer is trigonal pyramidal.