Hi
Hopefully I can shed some light on this for ya 
700x23 are sized for road bike rims, so I don't think those will work on your rims unfortunately.
The 700x23 is the size of your tire in centimeters (23cm is the width). I believe the other numbers are inches(?) Someone correct me if I'm wrong there.
On my road bikes I have 700x25 on my commuter and 700x23 on my "faster" bike. You do have some range in what you can put on a rim, but only so much. Because you have wider rims (38cm) you'll need to get wider tires. You can probably drop a little bit in size, but I'm not sure what the narrowest tire is that will fit your rims. You can also go wider than 38cm. Your tubes are also bigger than tubes that would fit a 23cm tire.
So the long answer to your getting slicks question is yes, with a little bit of flexibility either bigger or smaller. But not as small as 23cm. Does that make sense (I hope)?
I put continental slicks on my mountain bike, and they work fine. They're still not as slick as a road tire, as in there's still some minor tread.
As for the slime, there's a debate in the cycling community if that stuff is effective. Every LBS person I know says to never buy it. But maybe it's more effective in the wider tires. So I personally don't use it.
Good luck
"Only the meek get pinched, the bold survive"