Hi, I've read your job description and I can help you with this project because I have 5+ years of experience using Arduino and interfacing it various GSM/GPRS modules like Sim800L/900. For your task, apart from the easier part of setting up a proper SMS communication, we would need to use Arduino's built-in EEPROM as a database for storing user contact numbers otherwise they would get lost upon power failure. The other easier option is to use an SD card with the Arduino but that would increase the size of the unit which you don't want. To facilitate, insert, delete and view functionality of contacts stored in EEPROM we need to keep track of where a number is stored on memory, re-adjust memory when a contact is deleted etc.
For Arduino board, I would suggest Arduino Nano as it has a smaller form factor and suitable EEPROM space to load out contact list to it.
These are main issues to be addressed, remaining are logic issues which can be catered for in the code. For example we would be using some code like "DEL +1 xxxxxxxx" to delete the contact or "ADD +1 xxxxxxxx" to insert a new contact etc.
Regarding the alarm, I think it should be 12V signal for arm and 0V for disarm, please confirm. We can level 12V down to 5V using very cheap resistor-only circuit, so that won't be an issue.
Please let me know of further details so that we can continue. Thanks.