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I have different examples like these:
1) Pensé que era normal
2) Era increíble que ese perro supiera hablar
Why fuera instead of fue? Why supiera instead of supo?
Is this always the case, or are there instances where the indicative for the 2nd verb would be used instead of subjunctive?
Your first example isn't an example of two past tense verbs, but in the second one it's the simple rule of opinion + que + subjunctive. In present tense it would be "es increíble que ese perro sepa hablar". When the first clause is past tense, the second one becomes past subjunctive.
In reply to your first question (sentence (2) has been correctly explained by @polyglottera), you can find the answer on this forum.
I will provide a summarized translation of some portions I find relevant to understand the case at issue:
When in the affirmative form, verbs of physical or mental perception require the subordinate verb to be in the indicative mood but there are some (including parecer, admitir, conceder, aceptar, suponer, sospechar, imaginar, creer) which can take the subjunctive when reference is made to some fictitious, imaginary or alleged situation. When the content is more of a belief, the subordinate is conjugated in the indicative, but when it is merely a conjecture, the subjuntive can be used. The mood that prevails is the indicative and, in case of doubt (mainly among non-native speakers of Spanish), the subjunctive should be avoided.
The page I've quoted says that the subjunctive is usual when the main verb is in the imperative. I've included those examples that can be deemed to be similar to the one provided under (1). Indicative and subjunctive in the subordinate are usually equivalent, but the subjunctive sounds slighly more hypothetical or unreal:
Supongamos que diga que no.
Supongamos que se había casado con otra.
Supongamos que se hubiera casado con otra.
Figúrese que nos quedamos aquí.
Figúrese que nos quedáramos aquí.
Supongamos que está enfadado.
The sentence:
clearly conveys the idea that somebody or something is NOT normal, but the person is encouraged to think of him, her or it as normal.
Preterite subjunctive is even more hypothetical or unreal than the present subjuntive. If somebody or something is not normal, their normal status is completely contrary to fact, and this leads to the use of past rather than present subjunctive.
