The seal on the top of the pump doesn't really matter. It'll pump without the seal. There's a rubber 'slinger ring' which slides down the shaft and rests atop the upper pump housing. All this does is keep silt/debris off the top of the pump, hence the 'slinger' name.
The real sealing is done between the round ridges molded into the rubber impeller and the stainless plate at top/stainless 'cup' insert at bottom.
Check the center of the plate and also the cup, if there are large grooves worn into them, or obvious wear anywhere else, replace.
Clean up the rusty driveshaft so that the new impeller slides smoothly all the way down. You don't want it to bind on the shaft or you'll never get it properly in place.
Pull the gearcase oil drain plug and check the gear oil for water instrusion. If the oil is full of water, the driveshaft seal is probably shot. The lower pump body and copper water intake tube just pull out. The pump is sealed into the gearcase with an O-ring, and the oil seal is pressed into the pump.
Drive out the old seal and drive a new one in. A socket sized to just barely fit the diameter of the pump will easily drive the oil seal into place. Be sure to note which way the lips of the seal face and install the new seal the same way (should be with lips of the seal facing up).
This is just a basic overview, if you do a search you'll find more comprehensive directions on the job.
And as far as the motor goes, you can't complain about a $25 motor that runs! Even if the lower unit is marginal, you could test run the motor to see if the powerhead runs good, if so you could always upgrade to a newer lower unit with stainless shafts. Plenty of them on eBay or check your local
www.craigslist.org for used bargains.
HTH & G'luck with the repairs..........ed