Questions & Answers about Tror du att batteriet räcker tills vi kommer hem?
Because this is a yes/no question in Swedish. In main clauses, Swedish usually puts the finite verb first in yes/no questions.
- Statement: Du tror att batteriet räcker.
- Question: Tror du att batteriet räcker?
So tror comes before du because the speaker is asking Do you think ...?
Att here means that and introduces a subordinate clause:
- Tror du att batteriet räcker ...
- Do you think that the battery will last ...
In everyday Swedish, att is often included here and sounds very natural. Sometimes it can be omitted in speech, especially in casual language:
- Tror du batteriet räcker tills vi kommer hem?
That is also understandable and common, but att is the safe and standard choice for learners.