The most natural sounding alternative phrase is "We will figure this out." For example: "Paul, how can we stop the computers from crashing?" "I don't know, Jim, but I'll figure it out."

It means "We'll understand this." It is typically used when referring to a situation that is both confusing and bad. For example: "I found a $200 charge on my credit card that I didn't make. How could this happen?" "Don't worry. We'll get to the bottom of this." You can also say "We'll figure this out."

Hi, 'To get to the bottom' of something means to find out something: example "We got to the bottom of why the computer kept crashing", "The detective got to the bottom of the mystery". Another way to say it could be 'to find the cause of', or maybe 'to find the root of'.