Can I play on cracked servers with legit key (yeah I still have one ^^) ? Yes
Is there risk of global ban there? Yes, BattlEye is enabled (require as of 1.7.2.4, and unless you run the server and are running Darky's server hack, you can be global banned)
Is BE activated there? Yes, it is the same BattlEye that runs on official servers
My character is not downloaded from the global hive there right, it's unique to the server? True