Learn Turkish: Onlar şimdi fısıldaşacaktır. - They are probably whispering to each other right now.

When you combine the future tense (-acak) with the generalization suffix -tır, it expresses a strong guess or deduction, much like saying "must be" or "will be" in English (e.g., "They will be whispering right now"). Because it conveys a deduction rather than a literal future event, it can safely be paired with a present-time word like şimdi.

How does the verb fısıldaşmak differ from fısıldamak?

The added -ş is the reciprocal suffix. While fısılda- simply means "to whisper", adding the -ş to make fısıldaş- changes the meaning to "to whisper to each other" or "to exchange whispers".

Since the translation says "to each other", shouldn't the Turkish sentence include the word birbirlerine?

It isn't necessary here. Because the reciprocal suffix -ş is built right into the verb (fısıldaş-), the "to each other" meaning is already fully covered. You could add birbirlerine for extra emphasis, but it is completely natural to leave it out.

Could I say Onlar şimdi fısıldaşıyordur to mean the exact same thing?