“When we have been overwhelmed with emails, we wonder whether we might have missed something important by dealing with them quickly.”
In this case, whether and if are interchangeable. In both cases, there are two possible outcomes implied - either we missed something important, or we didn't.
“When we have been overwhelmed with emails, we wonder whether or not we might have missed something important by dealing with them quickly.”
Using whether or not is viable here too. It is equivalent to saying "When we have been overwhelmed with emails, we wonder whether we might have missed something important by dealing with them quickly or not." Instead of implying the two outcomes, they are being explicitly stated.
“A librarian can help you if you are wondering whether a source has the information you need.”
This is actually the same principle as the prior examples. There are two outcomes implied - a source has the information you need, or it doesn't. You can use whether or whether or not interchangeably. The only reason not to use if here is because it was already used earlier in the sentence and would sound unnatural.
An Additional Note
Neither of these examples have both outcomes explicitly stated in the sentence. Take this sentence for example:
We don't know whether Julie will arrive on Monday or Tuesday.
The sentence explicitly states two possibilities, one of which will occur. Julie will either arrive on Monday or Tuesday.
We don't know if Julie will arrive on Monday or Tuesday.
Depending on how this is read, there is now a third option - maybe Julie won't arrive at all.
In this case whether more clearly conveys the intent.