A couple things...
1. If your nitrate readings were truly 80ppm before your 10% water change, then they can't be 5ppm now. One of those two readings were off, and there's a pretty big color difference between 80 and 5 if you're using the API test kit - which I think I remember you are. You probably realize that, but thought I'd point it out just in case you didn't. Either there was some "user error" there, or you have an old test kit.
2. Good to see your ammonia is dropping from those high levels. Looks like your nitrites are getting ready to start heading up for a spike. Seems like your cycle is progressing nicely.
3. If you're trying to test the salinity of your saltwater immediately after you mix it up, it's hopeless. Until you let it sit (preferably with a heater and powerhead in it) for a day or so, adjusting the salinity is useless - it's just too unstable. Same goes with the pH. After about 24 hours of aging, you can check the parameters and adjust as needed. And as mentioned previously, a hydrometer is going to make it tough no matter what. A refractometer is a really really really good investment. All you need is a drop of water and about 10 seconds of your time and you've got your salinity. It's probaby the most useful thing I bought for my tank.
4. Depending on what salt mix you're using, a 1/2 cup per gallon usually gets you to about 1.021 SG. For Reef Crystals, I mix 2 cups salt with 3.5 gallons water and I get a salinity of 1.025+ and after a day or two I add some DI water to lower the SG to 1.024. In my opinion, it's way easier to purposely mix it saltier and then just add fresh water to lower the SG versus having to add salt mix to make it saltier. Add salt gets you back to the issue from #3!
Oh... and running the skimmer now won't hurt anything. It's a good time to get it broken in. Then again, it's no big deal if you don't run it either!