You cannot get out of the lock
There are always three ways out, and they do not depend on each other. The gesture
on the screen — hold, or tap the number of times you chose. The Unlock button in the
notification, then slide the circle to confirm. And if the touchscreen itself is
misbehaving, turn the screen on three times within five seconds with the side key:
that one never goes through touch.
The lock turns itself off after a while
Almost always the phone closed the app in the background. Xiaomi, Oppo, Vivo, Huawei
and Samsung each have their own rule — autostart, sleeping apps, adaptive battery —
and the app names yours on its own screen. Excluding Touch Protector from battery
optimisation is what fixes it. If you have already done that, tell me the phone and
the Android version.
The music still skips on the lockscreen
On the lockscreen Android hides the lock, and no ordinary app can change that. The
way around it is not getting there: keep «Automatic screen lock» off in the settings
— it is off by default — and use blackout mode, so the screen stays on and dark
instead of locking.
You can still pull down the notification shade
That is on purpose, and it is Android's choice before it is mine: no ordinary app
can cover the shade or the navigation bar, and they are your way out.
The home page explains the rest.
The tile is not in my quick settings
Android never adds it for you. On Android 13 and up the app has an «Add to quick
settings» button that asks the system to add it; below that you add it by hand from
the pencil or the edit button of the panel, where the unused tiles are. It is called
Touch lock.