What can I do with Account Extended Private Key and Account Extended Public Key? I have been reading about Account Extended Private Key and Account Extended Public Key that derives from the Master Private Key and Master Public Key, but I still have some question about their security.

I read that Account Extended Private Key should be kept private because if others got hold of it, they could sign the transaction with the key, effectively stealing your cryptocurrency. How does this work exactly? Is there an application that I can import other's Account Extended Private Key and send certain amount to my other wallet's address?

Also, I read that Account Extended Public Key should be kept private as well because exposing it to others allow them to go through the transactions. How does this work? Is there an application that I can import to view the transaction history?
I read that Account Extended Private Key should be kept private because if others got hold of it, they could sign the transaction with the key, effectively stealing your cryptocurrency. How does this work exactly?
  
  Also, I read that Account Extended Public Key should be kept private as well because exposing it to others allow them to go through the transactions. How does this work?


Extended keys allow for private and public keys to be derived from them. This is done using the algorithm described in BIP 32.

Your Account Extended Private Key is used to derive child private keys which are the actual private keys for your addresses. If someone gets ahold of this extended private key, they can derive all of your private keys and thus spend your Bitcoin.

Your Account Extended Public Key can be used to derive all of the child public keys in a similar way to how the Account Extended Private Key can be used to derive all of the child private keys. Knowing the public keys means that the addresses can be derived and thus anyone who has your Account Extended Public Key will know all of your addresses. They can thus observe every single transaction you receive and make.


  Is there an application that I can import other's Account Extended Private Key and send certain amount to my other wallet's address?
  
  Is there an application that I can import to view the transaction history?


You can import extended keys (public or private) into Electrum which will scan the blockchain for transactions related to child keys derived from those extended keys.