Neither / Either

1a. Neither of us likes him.
1b. Neither of us like him.
2a. Either of the days is fine for me.
2b. Either of the days are fine for me.
3a. Do neither of these sentences work?
3b. Does neither of these sentences work?
4a. Don’t either of these sentences work?
4b. Doesn’t either of these sentences work?
Please correct the above.
Thanks

Neither and either when used as subjects are always singular, so 1a, 2a, 3b, and 4b are correct, the rest are incorrect.

I’m in full accord with you, Luschen though it has been debatable.