Glossary:
System property is the property to manipulate with adb shell getprop/setprop command.
Device property is the property to manipulate with "Device Preferences" tab in WebIDE (requires privileged mode).
Device setting is the property to manipulate with "Device Settings" tab in WebIDE (doesn't require privileged mode).
To turn on ADB and WebIDE access without jailbreaking, you can use *#*#33284#*#* (*#*#debug#*#*) secret code.
Enable network type selection for both SIM cards
By default, Nokia 8110 4G allows you to only select 3G or 4G network for the SIM that has data transfer enabled, other being always 2G. To enable selection of all network types for both SIMs, issue the following commands:
adb shell setprop persist.moz.ril.0.network_types gsm,wcdma,lte
adb shell setprop persist.moz.ril.1.network_types gsm,wcdma,lteadb reboot
After reboot, you should be able to select any combination of network types for both SIMs in the "Mobile Network & Data" settings submenu.
Turn off the second SIM
If you own a dual-SIM version of 8110 but never need another SIM card, you can switch the phone to a single-SIM mode to conserve some battery life. To do this, run the following commands:
adb shell setprop persist.radio.multisim.config none
adb reboot
After reboot, the phone will completely start acting as a single-SIM model.
To change the settings back, you'll need to run:
adb shell setprop persist.radio.multisim.config dsdsadb shell setprop persist.moz.ril.0.network_types gsm,wcdma,lte
adb shell setprop persist.moz.ril.1.network_types gsm,wcdma,lte
adb reboot
If the data transfer settings still cannot be restored to the second SIM, you might want to run the adb shell setprop persist.moz.ril.1.network_types gsm,wcdma,lte command again and reboot or perform a factory reset.
Service boot modes: recovery and EDL
Nokia 8110 has a recovery mode (it has no fastboot mode though as of now - it's blocked from the firmware). Recovery menu can be accessed either with adb reboot recovery command or by turning the phone on keeping Up button pressed until the menu appears. It allows you to install patches from both sideload interface and SD card (as of now, recovery is not so secure: update.zip archives just must be signed with test-keys from AOSP 6.0.1_r3, I even created Stockerize tool package to help with signing), view boot and kernel logs and wipe data and cache partitions.
EDL mode, on the other hand, is a Qualcomm-specific "emergency download" mode that can be only entered with the undocumented adb reboot edl command. When you reboot into it, you'll see nothing but black screen, but it's normal. It's designed to be operable only with proprietary Qualcomm tools. To exit this mode, the easiest way is to plug the battery out of the phone and to put it back, and then turn the phone on normally.
Other found tricks will be appended here or in the replies.