Ok, here's what you can do:
Wind the yarn that you frogged around the skein. That's what I always do when I've frogged or tinked something and I've never had much of an issue.
Knit a swatch in garter stitch (all knit stitches) and one all in purl stitches so that you can get the hang of working those two stitches separately. I think that part of the issues you're having might be that you're trying to put stitches together too soon.
Invest in a darning needle and run a line of thread through the last row you KNOW you did right before you continue. That way if you screw up you won't have to frog the whole thing.
As far as putting the needle back into live stitches after you've frogged, well, you just thread it through. Once you come to knit (or purl) the stitches it'll be obvious if you have the twisted or not - and you'll be able to untwist them using the right needle. You slip the stitch off with the right needle by inserting it into the FRONT of the stitch, slipping it onto the right needle, then replacing it back on the left needle where it belongs - and then you can knit it.
If you are ever, ever within an hour or so of St Louis, give me a shout and I'll come meet you and we'll have a knitting lesson. I think that'd be kinda fun...