If you have an account at minecraft and can play on two computers (the same account) together over LAN?
Should be impossible. I never tried.
One should still be able to play on a local server that does not check accounts with a premium account and an offline profile. But if that works, it's harder than it used to be.
No.
Can't.
Would not synonymous sense then you would have to buy the game so only once.
Cracked can be played with the following launcher, ie Without a purchase account:
https://mc-launcher.com/special/minecraft.html
The Launcher can use Official, Cracked, Ely.By and MCleaks accounts.