What is

I see the videos, about increases, but, I’m not sure which ones to watch, in order to learn how to
work a right slanting M1 increase,
a left slanting M1 increase,
do a right slanting lifted increase technique,
and a yarn over increase.

And, what’s the selvege edge?

Why would long tail cast on be preferred over a thumb loop cast on,
or, my favorite, the cable cast on.
Doesn’t the cable cast on use more yarn, than the long tail?

so many questions. i dont know witht he increases/decreases ( im bad at them) but for the cast ons, i beliee that the ling term is often preffered because it is relatively easy to learn and to do and is a good general cast on suitable for many types o work, which is also unobtrusive. i discovered i quite like the cab;e cast on too, and might start using that as an alternatie when somthing wants a slightly more structured edge.

The long tail and cable cast on provide a more stable, firm edge than backward loop. They both use about the same amount of yarn. For the increases you want, look at M1R and M1L; watch MLR/MLL for the slanted ones, and there’s a YO.

The selvedge edge is just the sts on the ends of the rows. There is no selvedge st per se; some patterns may designate 1 or more sts as the selvedge, to be always worked in stockinette, garter or seed st, or slip the first st and knit the last.