The kanji for せんたく are incorrect in the example sentence. It should be 洗濯, not 選択. (:

I have recently heard this with the more polite ikemasen instead of ikenai.
shinakutewa ikemasen - must do it

in the Baic Construction, what is the bit with the VE/10?

Is

Ive never really thought about it. is there a way to make this form in the past
such as "i had to go"

thank you soo much.... sad to know ive been speaking this language forever and never...thought about this

くちゃ is more casual than くては, and yes, the は is pronounced わ there because it *is* a particle - literally this pattern is a double negative (you can't not do such-and-such) so it might be easier to think of it as なくて　は　いけません. いけません and いけないです are both correct, but the former is slightly more formal.

I don't think I've heard females using it more than males, but someone else might have a differing view.

Added it, thanks! Already had the てはならない on another page on the site, so it only makes sense to add this one as well.

essential sounds good to me! It does *kind of fit* if you think of it this way:

食べなくてはならない = we cannot have the situation where there is no eating = we must eat
なくてはならない = we cannot have the situation where there isn't (ない) = we must have it

漢字を練習しなくてはいけない

Is ないといけない relevant or not?