Ususally not. They don't place used equipment in people's houses so they have no use for it. They just abandon it.
2) If not, is it possible to use a different monitoring company with my current equipment? What monitoring companies can do this?
On these systems there is an installer access code which is required to get in and reprogram it for another alarm company. ADT has that installer code and will not give it to you.
3) If I can't use current equipment should I at least be able to use current sensors and just replace the keypad?
You will have to replace the keyboard AND main panel. You will certainly be able to re-use the original wiring and any magnetic reed type sensor or wired universal motion detector. Not any wireless equipment though
2 most likely - ADT doesnt make the alarm equipment .... either find the default installer code, or reset the board and change the code -- you'll need to check the security equipment box - it will have a label, google that model number and you will figure out the actual brand, then google installer codes for that model#/brand/adt etc (thats how i found the code for my "adt" system) . The other option - the security board can also be reset and installer code be changed ... i switched to alarmrelay ( i think their setup fee will include them helping you with above steps so you actually wont have to do it alone)
I reset my installer code on adt Honeywell/adenco panel by disconnecting power (both AC and battery) and do some button combination ( do not remember exactly what was it) within 30 sec after powering on again.