My front door got kicked in and split the door frame. I'm opting to just replace the entire door and frame. My question is
a) is it possible to just replace the split part on the door frame and if so, how to go about doing that?

b) if I replace my front door and frame, what tools are needed to accomplish this?

Yes, it is possible to replace the frame only. It is also possible to replace only the damage part of the frame, which is probably the lock side jam only. To do so depends on the damage done and your skills. Tools required would be the usual carpentry tools, hammer, saw, pry bar, level, tape measure.

Again depending on damage and what has to be replaced there should be two options.
Option one.

Remove and replace the damage leg. Right now I am assuming the lock sideonly.
Remove the interior and exterior molding. With a utility knife cut the paint and caulking between the wall and the molding and between the door jam and the molding. Using a small prying tool (screwdriver, putty knife, wood chisel) begin prying molding away from the wall starting at the bottom. You may or may not be able to remove it undamaged. Remove exterior molding same manner. The side jam will probably be fitted into a groove in the head jam at the top. It may also be trapped in place by the threshold at the bottom. If advantageous remove the threshold. Cut jam about center of height (if it isn't already broken in two). Pull and pry jam away from framing and out of groove in head jam. Jam material could be 3/4 thick material or thicker. You can make you replacement jam or purchase an unassembled door jam. If 3/4 material and the door stop is a separate piece, you can cut your own from 3/4 plywood but purchase a good grade with a sanded surface. If the doorstop is an integral part of the jam you probably should just purchase the unassembled door jam unless you have the tools to machine your own. If nails project through head jam in the groove they are probably finish nails and can be pulled through to remove. Cut replacement jam to length and put in place. Close the door. Place shims between the jam and the framing. One shim goes in from the inside and another goes in from the outside. Adjust shims to keep the distance between the door and the jam equal along the entire edge of the door. Nail through the door jam and the shim into the framing. After replacing jam you must bore hole for doorknob and lock bolts striker plates. Remove the doorknob and lock including the bolts. Measure boltholes, probably 3/4 or 7/8 could be 1". By a dowel that size, cut off about 1". Drill small hole in the center of the dowel and put a nail in it. Put dowel in bolthole, close door and tap nail to mark center to drill for striker plate. Reinstall bolts for doorknob and lock. Close door and mark height of striker plate on jam. With sharp chisel cut mortise for striker plates.

If you choose to replace the entire frame remove the interior and exterior molding.
Remove the door from the frame. Remove the doorframe. Purchase an unassembled frame kit and threshold. I prefer the adjustable thresholds. They are available in both aluminum and hardwood (mostly oak). On a work surface, assemble frame around door. Tack a 1/8" thick spacer to the top of door. Push door up against head jam. Set threshold to mid range of adjustment. Carefully measure and cut threshold to length. Measure the distance between the side jams at the top of the door. Assemble threshold to side jams.
Now you must carefully mark and cut the mortises for the hinges. Use a utility knife or scratch awl to mark outline of hinge leaf. When done properly the mortises hold the hinge in place and the screws hold the hinge in the mortise. Install the door and frame as a unit.