How can I disable Phone, SMS, Market and 3G functionality from Android?
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');
.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.