Authorize.net changes
This isn't a full answer, but ... I just had to research this same thing for a client.


Check that your processor config is using the correct URLs:
http://www.authorize.net/support/akamaifaqs/#newurls


/civicrm/admin/paymentProcessor?reset=1


Even in our client's old version of CiviCRM, the transaction ID field is 255 characters. 
The cipher suite is a question for your host. A good host should be using modern cipher suites and disallowing insecure ones. 
Not sure about requiring sequential transaction ID ... have not done a CiviCRM code audit to make sure (yet). Don't see why it would, but who knows.