Learn French: Pensez-vous que cette approche soit efficace ? - Do you think that this approach is effective?

In the affirmative, penser que does take the indicative because you are stating what you consider to be a fact. However, when you turn it into a question, especially using formal inversion like Pensez-vous que, you are introducing doubt or asking for an opinion, which triggers the subjunctive (soit).

Would I still use the subjunctive if I asked this without inversion, like Vous pensez que...?

Generally, no. In everyday spoken French, if you ask a question using rising intonation (Vous pensez que cette approche est efficace ?) or with Est-ce que, the indicative is much more common. The subjunctive is strongly tied to the formal inverted structure (Pensez-vous que) because the inversion itself highlights the theoretical nature of the question.

Why can't we use an infinitive here to avoid the subjunctive, like we learned previously?

You can only use the infinitive shortcut when the subject of both verbs is the same. Here, the subject of the first verb is vous, and the subject of the second verb is cette approche. Since the subjects are different, you must use que and conjugate the second verb.

Why doesn't efficace have an extra 'e' to agree with the feminine noun cette approche?

The adjective efficace already ends in an 'e' in its base masculine form. In French, when a masculine adjective already ends in 'e', it stays exactly the same in the feminine form, so no extra 'e' is added.