‘I couldn’t agree more’ is the normal expression. The version with ‘cannot’ is not used.
‘as well’ means ‘also’, ‘too’ : ‘James is coming as well’ [James is also coming, James is coming too’]
‘Are you learning Chinese as well ?’ [Are you also learning Chinese ? Are you learning Chinese too ? ]
In this context the two words ‘as’ and ‘well’ don’t have any meaning separately.
You can add ‘as’ to make ‘as well as’ : ‘David is coming as well as John’ [David and John are both coming]