Here are your parts includes a wiring diagram
Replacement parts for FRIGIDAIRE FRS22ZGEW2 | AppliancePartsPros.com

The evaporator fan usually stays on except when you are in defrost mode.
Usually half an hour or so every 8 hours.

Sounds like you have a defrost problem. The unit will run OK for a few days till the evaporator coils again get clogged up with ice/frost again.

This can be caused by a bad defrost timer, defrost thermostat or defrost heater.
The defrost timer looks like it is under the freezer side of the unit.
See Item 23 A in the "Controls) section (at bottom of the list)

Turn the cam till the fans & compressor shut off.
Note it only turns in one direction
You are now in defrost mode.
With the evaporator coil cover removed see if the element heats up.
Be careful do not burn your fingers.
If it does odds are high that the timer is shot.

Another test of the tiner is to mark the where the cam slot is, then leave it for an hour or so. If the cam has not moved the timer is not advancing so it is probably shot.

If it does not it could be the heater or the thermostat but this test does not totally rule out the timer as it's contacts may be shot.
Easiest way is to check the thermostat (0 ohms when frozen) and heater (usually around 20 ohms) for continuity using a meter.
Note the thermostat must be frozen as it open a few degrees above freezing.

Here is a good site with fridge repair help
Refrigerator Repair Guide: How To Fix a Refrigerator - ACME HOW TO.com

No if the heater comes on the defrost thermostat is OK as it is in series with the heater.

One proviso is that the defrost thermostat can go intermittent, often you can see that it is bulged out.

Keep an eye on the defrost timer it could be that it is hanging up at one spot in it's cycle.

Only way to tell is if the unit does not do a defrost which sounds like your original problem. I would probably replace the timer and perhaps the defrost thermostat just to be safe. The heaters rarely go intermittent.

The problem happen again tonight fridge is warm and there ice build up in the freezer and now it seems that the defrost heater is not coming on when I advance the defrost timer. How do I check to make sure it's the heater element or the timer.

You have an intermittent problem.
The unit is messing with you. Same principle as it is broken till a tech shows up, then it runs just fine.

The most likely culprits are the timer or thermostat.
I would replace both as the are not too expensive and it is cheaper than throwing out food.

Defrost timer in the "Controls" section shown as Item 23A at the bottom of the list = $17.89

Defrost thermostat in the "System" section Item 21 = $13.89

Glad to hear you beat the fridge.

I would put a post in the correct forum category for the freezer and the dishwasher with the model numbers.

Yes it could be there is ice in the freezer lid especially if the lid liner is cracked.
Many hinges on old chest freezers have some adjustment. Take a look for slotted holes or extra places for the hinge springs to connect.

Some rinse aid dispensers are mechanical re: a lever runs on a cam on the timer. Sometimes a spring can let go so the lever does not track on the cam, the result is no rinse aid.

Kenmore's are usually Maytag/Whirlpool they often use a wax motor to open the rinse aid. It has a piston that is pushed out by melting wax in a cylinder. Then as the wax solidifies it is pulled back in. Sort of like a slow moving solenoid. If the heater element burns out then the piston will not push out and you do not get any rinse aid. This is not uncommon. Remove one wire from the wax motor and check it for continuity. If open (infinite resistance), it needs replacing.