The sensor Honeywell TC807A 1036 (Smoke Detector), is compatible with a NFS-320 Fire Alarm Control Panel?

copy and paste
https://www.alarmgrid.com/faq/how-do-i-add-a-siren-to-my-honeywell-vista-alarm-system

Replace the battery and be ready to replace the fire alarm (smoke detector).
Depending on type of detector, it may be able to be taken apart, disassembled for cleaning. Cobweb, dust, etc. can upset the detector sensor eye.

Try down powering the smoke detector zone either at the panel or at the devices, then re-applying power. That should "unlatch" the alarm for the zone.

Kidde Dual Sensor Battery Operated Smoke Alarm PI9010

reference: http://www.kidde.com/home-safety/en/us/products/fire-safety/smoke-alarms/pi9010/

Before I can really try to answer, I would like to know what make/model control panel you have (ex: Honeywell Vista20P), the zone number of the affected smokes, and whether or not you get an indication of a problem on your keypad.

Intermittent problems are often difficult even for professionals. That said, I would need more specifics on the problem if you want to continue on your own first. The model of the system, keypad indications, whether the problem is a trouble or alarm, what make/model the detectors are (there could be more than 1 type on a 2-wire fire zone), etc.

This is not a beeping smoke detector. It is probably a CO detector that was installed by your alarm company. GE model 240-COE will give a double beep every 5.5 minutes when the device reaches end of life. Call your alarm company to have it replaced.

What type of smokes detectors are you using. Is the Zone programmed correctly. Loose connection. Missising resister

It is a common "problem" that really is not a problem at all! It means the sensors on your detector are working properly. The first smoke that comes off of a fire is moisture burning off. (that is why a fire smokes white/pale grey but the smoke gets darker as the fire burns hotter but then once firefighters attack the blaze with their hoses, the smoke returns to the pale color but thicker) Your detector was designed to go off upon early detection of a threat, which is mimicked by the bath steam in nearly every manner.

Your smoke detectors, heat sensors or fire pull stations (depends on what is installed in your system) are located on your 4 zones. The wiring that connects these sensors to your fire control panel is supervised by an end-of-line resistor. Starting at the panel all wiring on that zone is daisy chained between each detector with the resistor being placed at the last detector. The panel looks for this resistance value at all times. If one of your detectors goes into alarm this creates a short. This is how the system recognizes an alarm state. Conversely, if there is break in the wiring the system fails to see any resistance and the panel will indicate a problem or trouble condition. The most likely cause of your 2 problems is either broken or cut wiring, ie; the system no longer sees the end-of-line resistance. If you are handy and have access to a multimeter you can measure resistance along the zone loop by disconnecting the zone wires from the panel and measuring wire resistance from each detector to the last one. Most Firelite systems use a 4.7k ohm resistor so you should see this at the zone wiring from the panel. If you don't, try removing a detector somewhere in the middle of the circuit and try again. Once you find a detector with that resistance your problem lies between that detector and the panel. It is just a matter of isolating the problem by measuring the zone resistance along different points of the zone wiring. If you are not comfortable doing this by yourself then I would suggest getting either an electrician or fire alarm tech to track down the problem. Hope this helps.