How does the Spanish subjunctive work after verbs of knowing or believing (dudar, saber, pensar, etc.)?

Does "nunca dudaba que" take the imperfect subjunctive or the indicative? I've seen examples of both.

The Spanish subjunctive is sometimes optional after verbs of knowing or believing depending on the degree of uncertainty involved. If one is very certain, indicative may be used, if not the subjunctive is used.

Usually, the indicative is used with a verifiable fact. For example:

no sabía que él estaba en la casa.	I didn´t know that he was in the house. (demonstrable fact)
no sabía que fuera así.	I didn´t know that it was like that. (a quality or characteristic is hard to verify)

If the subordinate clause is or was in the future, the subjunctive is used:

No creo que él vaya a llegar a tiempo.

I don´t believe that he will arrive on time.

Complete the following sentences using either the imperfect or the indicative.  Although capitalization does not count, spelling does!

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1. No sabía que la puerta abierta. (I don´t think that the door was open.)

2. No creo que él deprimido. (I don´t believe that he is depressed.)

3. No pienso que el ladrón a confesar. (I don´t think that the thief will confess.)

4. No dudaba que él mintiendo. (I don´t doubt that he is lying)