If I understand you correctly, you have removed the internal hard drive from you MacBook Pro and inserted it into an external caddy. When used like this, the performance of the hard drive is much better. It sounds like the internal SATA cable is damaged.
There should be no issue with using an external bootable disk. While typically the performance of an external connection is slower than using an internal connection, your case is an exception.
As you said, keep the connection to the disk secure. If the disk is disconnected before shutting down, it could lead to file corruption, volume corruption, or other data loss.
To make sure it finds the disk easily during boot, I’d recommend:
- Connect the external disk before powering on the Mac arch time.
- Select the external disk as the default boot volume in System Preferences > Start Up Disk (you may need to unlock the padlock before you can select th disk).
Finally, I would recommend contacting Apple Support. If covered by warenty, AppleCare, or Consumer Law, service may be free. Also, if a repair program is available for this issue, it could also cover the cost of repair.