Is the disk formatted a HFS+ Journalled with a GUID partition map? You can get this information from Applications -> Utilities -> Disk Utility. The disk MUST have a GUID partition map, or it cannot be a bootable drive.
2/ Is it normal that a window appear saying CCC need my password to modify certain things before cloning process ?
To make a bootable clone CCC must be able to read ALL of the data on your disk, including stuff that is normally protected from non-priv'ed user access, so YES it is normal (essential) to need your admin password to create a clone.
3/ Is CCC's trial mode even allows to make a bootable clone ?
From the CCC web site: "...You can try the complete feature set of CCC for 30 days before purchasing it...", so Yes, you can create a bootable clone using CCC during the 30 day trial.
Carbon Copy Cloner is a very good backup utility, and has earned a strong solid reputation over the many years it is been around (I use it daily).
If you want, you could try SuperDuper, which allows a full clone for free, and you only need to pay for it if you want the incremental update and scheduling features (SD is also a very good solid cloning backup utility; that I also own and use).
There is one solid advantage with CCC, in that it will also backup your Recovery Partition.