Yeah, the Tomos has two adjustors on the back wheel bolts, tighten em down a bit, and then use a rubber mallet and an unsharpened pencil to get em nice and tight, so there's only 1/2" of slack.
You tighten the bolts some FIRST, so they hold it in that position and it doesn't come loose again while you're spinning them tight - see ?
As for the chain, yeah, if you can find the master link on it, you can blow out a couple links if ya have to, but check other stuff first...and if it's that loose, make sure you didn't crack any teeth off the sprockets or misalign your rear wheel in the process.
As for Tubes and alla that, I use BELL Self-Sealing...available at yer local Walmart, technically bicycle tubes, but if you get em an inch or two bigger than your wheel really is...they work damn well on mopeds too.
(you can use exact size, but it's a bitch to put them in that way.)