The metal deflector above the burner flame in the tube is rusting, scaling and overall thinning, does this mean a new water heater or can it be repaired? Thanks

I presume you're talking about a gas furnace, even tho the title says Rheem gas water heater. Either way, it works the same for both.

Any black coloring on the heat exchanger is *not* from overheating. Black is from a sooty flame caused by a mis-adjusted burner. (In fact, a sooty flame is less hot). There is an adjustable "air intake plate" for air to enter the burner where the gas enters the burner. A proper flame is made by adjusting this air opening so the proper gas/air mixture feeds into the burner. If the air vent is closed too much it produces a sooty flame.
The age of the furnace is the most important aspect, and that helpful to determine a likely condition of the heat exchanger and burners. Other than a badly adjusted flame, the main thing to watch for is a badly rusted out heat exchanger. But black does not mean rust.

There is a sensor that shuts off the gas to the burner if a flame isn't detected within a few seconds. It will usually look like a tube that extends into flame of the burner. It may be defective or it may just need to be repositioned so more of it is directly in the flame.

Sounds like the sensor is not working shutting down too early

Clean burner tube with proper brush, such as long spring type for bar-b-Q burner tube that are available at most hardware stores, and make sure you have new burner tube aligned properly (straight on) with brass orifice on gas control. Then be sure to adjust air shutter for nice blue flame, with little orange at tip. Do not give so much air that flame roars or jumps off the end of the burner tube. Too many people think more air, less fuel, but actually, when flame roaring and jumping off end of tube, the heat passes through faster and it takes longer to heat the water inside the tank. Like I said, only enough air to have quiet, steady blue flame. If your not giving it enough air, you'll see dark soot on trailer above water heater, which indicates burning too rich, need more air, or perhaps pilot is partially plugged. Pilot flame should also be blue, not yellow/orange. Small air intake hole on side of fitting just before pilot tube can get spider web, or debris in it as well. Use air to blow that out or a piece of wire like a paper-clip to clean inside that hole.

Clean the burner and burner tubes.
http://waterheatertimer.org/How-to-install-gas-water-heater.html#clean

Read your manual for maintenance and troubleshoot steps

The difference between an orange flame and blue flame is the amount of air in the combustion process. SO if the flame is orange it is being starved of oxygen. The gas burns dirty and soot is generated.

Sometimes with an older heater the exhaust venturie becomes plugged and carbon monoxide is released into your home- in this case your heater would make a woof or poping sound when starting up or shutting off. This is a dangerous unsafe situation and professional help is needed.

What you can do is try to make adjustment yourself, if your confident the other situation does not exist. Your water heater should have a little deflector shield on the gas line between valve and burner (typically immediatly after the orfice). Sometimes these will have to be slide front or backwards or twisted. The adjustment of deflector shield must be opened more to make the blue hotter flame to mak eyour heater operate at peak efficiency.

Good Luck

Look at the flame and see if it's burning blue or yellow. And then see if it's burning all the time. If the flame is yellow and water heater does not make hot water, the thermostat may keep the flame going all the time and use up your gas.

Poor flame color means you should clean the burner or replace the burner. If water heater is exposed to trace amounts of some chemicals, like bleach or pool chemicals or wax, these chemicals get pulled into the burner and will shorten life of burner assembly and combustion chamber.

If the flame is blue and the water is not hot, then the thermostat is the best suspect. The thermostat is part of the gas valve. The gas valve has a copper tube that extends into the water and reads water temperature. If thermostat reads incorrect temp, then the gas valve needs to be replaced with gas valve from local plumbing supply of Lowes.

If the flame is blue, and it runs all the time, then your tank may have a layer of sediment between the flame and the water, and the sediment has caused water heater to become very inefficient.
http://waterheatertimer.org/Clean-sediment-out-of-water-heater.html

Now to answer your question:
You can turn up the thermostat dial located on front of tank.
Check your flame and how often burner comes on to determine where problem is.
You can buy a gas valve from Lowes for $65 or from plumbing supply and then replace >> you need a couple wrenches and pipe joint compound and about half a day.
You can clean the burner with wire brush and shop vac.
Remove chemicals from same room as water heater.
If the water heater has sediment build-up, then a new water heater is probably best choice.

You can do some things yourself. If the do-it-yourself steps don't work, then get a new water heater, and you know more about maintaining a water heater because you worked on the old one. Save the new water heater manual. Read the manual because it has ordinary information that will save you money long-term.

How to determine age of water heater
http://waterheatertimer.org/pdf/WaterHeaterSerialNumberDecoder.pdf

You need to have a manometer (pressure test) done on your system. If all that is new and clean, as stated, then you either have low pressure or a faulty/improper, gas control.How's the flames look on stove burners?

Sounds like the burner flame may be too strong (jumping out from burner tube) . Some people think the louder the better, but that is not correct. When burner shuts down like that, it has a tendency to snuff out pilot as well. Adjust your air shutter at burner so that the flame is a nice blue, or with just a hint of orange/yellow at the tip. Whatever setting that keeps the flame solid from burner tube, and not a big gap between tube and flame. Signs of soot (black) up the cover, or side of trailer means it's running too rich, and you've gone too far thus needs more air. Keeping the flame blue but still right out of the burner, actually heats better, is quieter, and should eliminate that pilot getting snuffed out. Pilot should also be a nice blue flame as well. There may be a problem with positioning of the burner tube as well, but doubtful if it has been running well in that position before. Let me know what happens.

For the main gas valve to come on several conditions need to be met.

The system must detect a pilot light prior to turning on the main gas valve for systems with a standing pilot light (not sure what your system has) and on systems with auto igniters (spark or ceramic heat glo) the control board must detect a flame present at the main burner a few seconds after the main gas valve turns on.

The other condition that must be met on systems with power exhaust systems is a vacuum/pressure diaghram switch must be made and stay made telling control circuits that vacuum/pressure is present = power exhaust fan is on and working.

From your description it sounds as if you may have a dirty/failing flame detector (thermocouple). Remove it and give it a good scrubbing with a scotch brite pad etc. cleaning off any carbon or corrosion/gunk re-install and try it out, or simply spend $15.00 or so and install a new one to be sure. The thermocouple is the metal thin tube that protrudes into the pilot and/or main burner flame and is connected to the main gas valve by a thin capilliary tube.

To check the vacuum swich on the blower a multi meter across the switch terminals looking for a steady "state change" as the blower runs/stops will work.