Your questions have more questions within them, and to do justice would require very detailed explanations, in other woods, too much for simple answers here.
Your scroll saw is less of a "woodworking tool" and more of a craft tool. You can do some woodworking tasks with it, but it's very limited.
Harbor Freight clamps are OK, I have some of their squeeze types, but they run out of "grip" sooner than later. Their other hand tools are OK. I've had great luck with their angle grinders, but I don't use their stationary power tools. Used cast iron Craftsman is a better source for power tools.
You will not have any luck sawing 2 X 4"s into narrow strips, no matter what tool you use. You are better off to purchase those narrow strip pre-cut that way they are already dry and will warp much less.
You will need to understand how wood behaves, moves, and cuts and that's a whole "book" in itself. The different species have different properties ... Oak is different than Pine etc.
Hand tools vs powertools?
My shop has a both, and I find that for preparing large wood planks form rough sawn lumber I use the power tools almost exclusively. Hand saws and hand planes are used for touch up and trimming, not ripping, jointing, crosscutting and thicknessing or planing.
This video will get you started with the basic handtools:
As far as basic power tools, that's a whole 'nother book, too much to cover here in a paragraph. Again check out You Tube to get started. The Wood Whisperer" has some good videos and gives clear explanations. You will find that a table saw is the heart of a woodworking shop and you will need to get one eventually. Table saw safety is a whole 'nother very long topic. There are threads on that here, check them out.