[Q] How to gain root with superuser without access to device screen

I have a Japanese Sharp 005SH Android phone. Currently, the phone had been locked up at the start screen due to the phone being out of network service for a long time.

I have rooted the phone before, and have SuperUser installed.

Currently, I am trying to get rid of the screen-lock service by the publisher by using the command "adb shell am start -a android.intent.action.DELETE -d jp.co.sharp.android.secure.StrongBox"

The problem now is. whenever I enter adb shell, the prompt is $ sign. When I type "su", nothing happens, and the cursor just blinks. I guess that this means the SuperUser app on the android phone has come out with a prompt which I need to touch to grant access. However, this is not possible as the screen is locked by the aforementioned publisher service.

Question
1. Is it possible to gain root access through ADB with the device screen locked?

2. Is it possible to remove the publisher's service without root access (and with the screen locked)?

Thank you for your time in reading this post.

Warmest Regards