Bushy260 most commendably gave the 'magic numbers' in the OP.
1999 manufacture
should be US-made, but we have our suspicions about any engine with a 'plant number' [the last two digits of the Code] in the 50's being early Chinese-made examples. The early Chinese engines had a few quality control issues...
2002 is the changeover year [for their small sidevalve engines] that Briggs give, but there is reason to believe that this may not be definitive.
The partly sheared flywheel key will be due to the blade striking some solid object - always an issue with this blade type. And it's one reason that that key is a 'designed weak point', and made of soft alloy.
Replacing the key, as you say, will have fixed any spark timing issues.
And it sounds like the primer is working OK - as vccomm says, what it does is to pump air into the float bowl vent circuit.
The usual reason that these Walbro carbies leak fuel out through the primer bulb hole, is that the needle/seat float valve is leaking. This can be due to muck, or to the soft neoprene seat having gone hard with age - and the age of the machine makes me suspect the latter.
For sure, take the head off to check for deposits - but it's not common to find much on the valve sealing faces.
Compression issues due to rings are not super-likely - as vccomm has mentioned, lack of tappet clearance [especially on the exhaust valve] is the next most common cause of hard starting in a Briggs, after carby and ignition.
Time to check these too, while the head is off - it's easily done, since the cowlings will all be off anyway.
