The first stitch you described is a SSK a video instructing you on how to do it can be found at
Knitting Help. The purpose is to twist the stitches so they don't look all loose and saggy (this would happen if you slipped both stitches purlwise). I prefer the SSK "improved" (also on knitting help) where you slip the second stitch purl-wise. I feel like it's a cleaner looking decrease. You can watch the videos and look at the examples to decide which look you prefer for your lace.
The second decrease is a handy double decrease that is centered (so it leans from both the left and right). You simply reach over the completed k2tog stitch on your right needle to grab the slipped stitch with your left needle. Then just lift it up and over the K2tog stitch and let if fall off of the needle. This is also demonstrated on the knitting help website as a "SKP aka sl1, k1, psso." The only difference is that you'll be doing a k2tog instead of k1. But that video will clearly show how to pass the slipped stitch over. One tip is to try and do this maneuver close to the edge of the needles so you don't have to stretch the slipped stitch out to pass it over the k2tog.
It's true that the SKP stitch takes 3 stitches to complete, but when you finish it you have only one stitch remaining. That's why it's all in one block.
Do you mind if I ask what shawl you're making? While I'm no stranger to charts I've not yet made an intricate lace shawl. I plan to fix that towards the end of this summer, though! I'm always looking for ideas of what shawl to knit.
Good luck, and do let us know how things are working out!
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