How can I check when was the phone rooted? In the adb shell command when I entered su, it prints:

su
root@hxjgeakt:/ #


It means my phone is rooted right?

How can I check when exactly was the phone rooted?
As for the first part: Yes, that definitely means your device is rooted.

For the second part of your question, IMHO it's close to impossible to figure the exact timestamp of rooting (apart from yourself noting it in some document). Though there seem to be tools reporting it, as mentioned in this answer1, I'm afraid that timestamp is not much reliable (unless I missed something). According to Andrew's comment, those apps do so by checking the timestamps of certain files, such as the su binary. Depending on several conditions, that might be totally off:


if those binaries have just been updated (e.g. SuperSU updates the su binary when new versions are available), that timestamp is definitely much later than the time you've rooted the device
if they have not been updated, it might report the time the binary has been compiled (depending on how it checks the file's timestamp)
I'm not sure how such an app could distinguish above two cases
if you have restored the device from e.g. a nandroid backup, it could again be wrong even if it checks when the file was "last written"


So if any tool tells you the date, I wouldn't count on the fact the date is correct – unless the dev can explain how the check is performed, and prove why the reported timestamp is correct.



1: the linked answer was deleted while I wrote mine