Can an employer write me up for 1. Not saying hello to a coworker or boss. 2. Not saying Happy Easter to a coworker or a boss?

Yes they can. Your employer can set reasonable expectations for polite behavior and you should do all you can to be polite and cordial. In most jobs the employer can also terminate you without giving a reason, called employee at will.

Yes and no. An employer can set certain standards of behavior, And as long as the standards are made clear to everyone and enforced for everyone.

However, since Easter is a religious holiday, there may be issues about religious discrimination.

You can be expected to say hello and speak to co workers and most certainly speak to your bosses.

You can not be required to wish people a Happy Easter, since it is a religious holiday.