You have small system for this!
What is charging cycle of 120Ah ? (theoreticaly if solar panel sits under street light solar panel give about 12A, 12hx12A=144Ah)
System on 12V for such amperage (wattage) is not good. System on 12V is for up to 500W not more. (500W/12V=42A on 24V system half of this).
One battery is ebough use bank of batteries and more power of panels.
Air Conditioner have motor inside, if standard HVAC thats very bad, use inverter tech. Standard have to high peak when starting compressor. For 12000BTU 1,5KW is enough You need 3KW or 4KW. Better consider inverter tech. compressor on 24V.
Also check standby current for that inverter of 1,5KW its about 1A I supose.
What battery You use? Consider multiple batteries. Lead Acid starter batteries should not be discharged complete. You say car battery 120Ah (Whata big car!). Every discharging under 11.9V kill batteries (its very very very bad for bat to go at 10,5V voltage level, starter is good for float discharging or about 70% not under this).
But DeepCycle can be discharge completely, but have smaller amperage on start, and ususally discharging at 20h, and they are very expensive. Calculate /10 or /20 discahrging time.
A failed cell in a parallel bank will sap energy as the other cells try to charge it. This can cause heat and loss of water in the failed cell as well as lost current capacity. The failed cell in series connections may add some resistance and, since it does not contribute any voltage, it will show as a reduced battery voltage.
Also consider up to 5 years life in float discharging, and for starter few days or one two weeks for starter if completely discharging.
Consider usage of desulfatisator.
Consider and put in calc losses and efficiency of inverter and all system this decrease battery amperage hour reserve. (probably will get to pull 20% more power on lower side).
For system always calc and consider following:
- input power (140W),
- condensator-bat of power (120Ah),
- consumer power needs (1,5KW),
- working time (for 120Ah, and 1,5KW at night You have theoreticaly few minutes of working time, and boiling of battery). LeadAcid batteries are designed for /10 or /20 time discharging. If You have 120Ah, 120Ah/10h=12A, 12A*10h=120W. You see now reason why people using lots of batteries in batteries bank (serial or parallel). If You go under /10 time discharge, declared manufacturer capacity does not apply, and curve of discharging time is much much different.
For stronger consuming needs from system, current is problem, and for this reason things goes to higher voltage, 48V 72V ... in electric cars is over 72V.
On Your system You can use smaller devices, such small lcd tv, laptop charger, table fan, CFL lights (but change CFL to LED (always use Warm White, not Cold White) lights, and other such smaller devices, even use of refrigerator.