Unit $4$ Block cipher modes of operation

Skills and elements used

Block cipher modes of operation $($ECB$,$ CBC$,$ OFB, CFB$,$ CTR$,$ GCM$)$

$1)$ What would happen in cipher block chaining if the IV $($Initialization Vector$)$ is not used?

$2)$ What makes CBC a bad choice for large plaintext inputs whose data needs to be randomly accessible, for example, a long audio stream where one might wish to jump to the end of the stream.

$3)$ Why is it important when using counter mode $($CTR$)$ to never reuse the IV $($AKA nonce$)?$

$4)$ What is the issue with ECB that makes it a bad mode of encryption to use even with a strong cipher such as AES?

$5)$ How does Output Feedback Mode $($OFB$)$ differ from Counter mode $($CTR$)?$

$6)$ Using DES for encryption with its $56$ bit keys a brute force attack would take at most $256$ attempts to find the key. If we encrypt the data twice, with $2$ keys des$($des$($p$,$ k$1),$ k$2)$ what is the new effective key strength i$.$e$.$ how many attempts would it now take $($worst case$)$ to brute force the key and why?