You can get a sprocket checker. The classical one was that by Rohloff but KMC and some other manufacturers have their copies of the tool out. Smaller cogs can indeed wear faster and you can principally replace just some, but it quickly ceases to make financial sense. Different operation for the new and old chains does not sound good and going back to the old chain is not a good solution. I would replace the cog and even chain now and already order a new cassette. When the drivetrain is not being cared for, 1700 miles for the lifetime may be close to normal. Else, with the new cog, you may wait till the 0.75% you cling to for the chain, but it may be a rather short time - the wear progresses at an accelerated rate.
I agree that the cassette needs to be swapped along with a new chain but... in another thread to OP asked about getting his zizzo a bit better. Since it needs a new cassette and chain, I would through in a new 9 speed shifter and a pair of ergo grips.
upgrading to 9Speed will offer a better range (wider range or closer gaps) for ~$40 extra.
That what I did with the kids bike, Altus 8 speed (11-32) swapped for acera/alivio 9 speed (11-36). I needs the sunrace cassette and the alivio shifter, derailleur worked (did it on 4 20"bikes so far).