Re: 1,2,3
Removing SIM card is the safest option, but you could try enabling modified airplane mode in the system settings : http://developer.android.com/reference/android/provider/Settings.System.html
in adb shell you could try :
su
sqlite3 data/data/com.android.providers.settings/databases/settings.db
insert into system (name,value) values('airplane_mode_on',1);
insert into system (name,value) values('airplane_mode_radios','cell,bluetooth''cell');
.exit
reboot
Re.4
Have you tried apps like https://market.android.com/details?id=com.vlobe.smartappcloud.android.parentalcontrol
You could also remove the Market app completely and only install apks via adb.