はずだ

はずだ means "should be", "is supposed to be": the speaker expects something to be true and has a reason – a timetable, what someone said, how things normally go. It follows the plain form; a な-adjective keeps な and a noun takes の.

• × 明日は休みはずだ → 明日は休みのはずだ

Expectation, not advice

English "should" also gives advice. はずだ never does: advice is ほうがいい and duty is べきだ.

• × もう寝るはずだ (as advice) → もう寝たほうがいい

はずがない

はずがない says there is no way something is true. It is much stronger than putting a negative verb before はずだ.

はずだった

In the past, はずだった is "was supposed to": the plan was there, and it did not happen. はずではなかった is "this wasn't supposed to happen".

A past verb before はずだ is different: it is a confident guess about the past.