How to do GREP text searching without root? There is busybox and there are terminal emulators that include grep, but they require root to run. It would be better if they could also run without root but with limited access. I only need to grep (read-only access) files in the user data storage.

Is there a way to do grep text searching on Android without root?

There are many text editors already, but they only support ordinary text searching by jumping to the text position, which is not nearly as convenient as grep, where one gets the desired results in a list at one place.
You are mixing up two things:


Installing a binary like busybox system wide from within an app (which includes grep)
Running a binary 


The default app based installers for busybox require root access to install busybox system-wide. This is true, however this is just because it is an app. Once the binary is installed you don't need root access.

Additionally even without root you can also install a busybox (or whatever) binary on your device:


You need to activate Android Debug Bridge (adb)
Copy the binary onto your phone (if it is not already there): adb push busybox /sdcard/
Copy the binary from the sdcard section (where it can't be executed) to different directory like /data/local or /data/local/tmp: adb shell "cat /sdcard/busybox &gt; /data/local/busybox".
Then make it executable using adb shell chmod 0555 /data/local/busybox


Now you can execute it using its full path from within a terminal app or inside adb shell:

/data/local/busybox grep ....