If I am rooted and if I boot into safe mode, will I be having root access and how to test that I have root access.
Safe mode only disable users app (non system apps) and let you troubleshoot which apps may be causing trouble.
And yes, of course you'll still have root access. The only way to check root is via adb command.
Install ADB (now available since Google released it without all the SDK), open a terminal and tape this command :
adb shell su
The output should be # instead of $