get a couple half yard pieces strictly for practice. Solid colors arec easier. Sale rack or Walmart $1 a yard stuff is fine. I'd get a lightweight cotton or polyester cotton, something heavier than that (medium to light denim is good), and something like corduroy which acts very differently than most non-strech fabrics.
The fiber content is on the end of the bolt (the cardboard insert), it's there by regulation along with laundry instructions, price and sku numbers as well as a bunch of other numbers that are used strictly in store & by the maker.
Put contrasting thread in the machine for this practice, and different in the bobbin too. Makes it wonderfully easy to see what you are doing.
E.g. white fabric with red thread on the spool & yellow in the bobbin. Do all experiments on a double layer of fabric.
Go through your manual and try everything
on all three fabrics. Do the zigzag, satin stitch, straight stitch, basting stitch, button hole, letters (if you have them), overlock stitch (if you have it), and anything else your machine may have that I'm not thinking of at the moment. If your machine has 75 fancy stitches, you don't need to do all 75, just do a couple to see how the system functions, the size, how long the machine takes to do it & such. Things like straight stitch & zig-zag you might roll a hem & see how they do on thicker layers too.
Not only will you get comfortable with your machine, you will know what it is capable of too
EDIT: adding stuff to go with your original questions
Pleats are all about measuring & ironing, the sewing part is as easy as sewing a straight line, they are very tedious to do, and it helps to be OCD to do them well :/
Piping is wonderfully easy! I always use a wider strip of bias cut fabric than I need just becase it makes the assembly a breeze.
To make 1/8 to 1/4 inch piping, get cotton cord (string) the size you want your piping.
Get or make bias strips 1 inch wide the length you want of your piping (total, you can cut it up after it's made). If you are using ready made bias tape iron the folds out.
Put your zipper foot (or piping foot if you have one) on your machine. [a piping foot and a zipper foot look very similar, like a ski, piping foot tends to be longer & slightly narrower]
Place your cord in the center of your bias strip, fold in half.
Place the folded strip with cord under the foot so the lump is snug up against the foot.
Start sewing! Keep the cord centered and the lump snug to the foot & it goes quickly
If you don't want all that fabric in the seam you can trim the excess from the piping, but I tend to sew it in place first and then trim.
You can easily scale up the piping instructions for larger things. I did piping for a chair and used 1/2 cord and 2 1/2 inch strips.