all you should need is a 1/4" or 5/16" socket, it's a bolt that goes into the engine block, be sure you're turning the bolt counter clockwise to loosen. I've got a pushmower with the same engine model.
Yep, 1/4" socket.
Briggs usually doesn't stamp the part numbers on their parts, you look up the parts online by using the model and type number 102802-xxxxx
For that motor it should be Briggs and Stratton 591420
Be sure to set the air gap between the legs and the flywheel between .006" thousandths and .010" thousandths. a index card or business card usually gets it close enough.
here's a link to the operators manual if you need it, https://www.briggsandstratton.com/n...ng.downloadmanual.277038-DOMESTIC_LO.pdf.html