The frequent cycling of the pump is very expensive- in terms of electricity use and the shortening of the pump life. So get that resolved first and soon.
Others may be more expert on home water treatment systems. Multiple filters do decrease the pressure when the water is flowing. In the worst cases, a booster pump could be used.

Well ownership 101:

1. It is difficult to tell because of the lack of punctuation, but it appears you have had your water tested for bacteria but nothing else, is this correct? If so, it is important to know a few more things for safety purposes: nitrates, sulfates, VOCs.

2. You way you want to removed sediment. In order to do this properly, we need to know what size/type of sediment we are dealing with. Is it silt (clay-like), sand, pebbles, etc and what size are the particles? Testing is a good thing here as well.

3. You mention wanting to remove iron. For this is happen, we need to know the amount and type of iron. Is it particulate or dissolved? This requires a test as well.

4. You mention wanting to use carbon to improve taste. Carbon may, or may not improve the taste of your water. It depends entirely upon what is actually in your water.

5. You mention the water has on odor. What type of odor?

6. If you want a complete, useful water test, test for the following: pH, TDS, alkalinity, hardness, ferric iron, ferrous iron, manganese, sulfates, nitrates, VOCs. Those are necessary no matter what treatment you ultimately decide to use.

7. You need to know some things about your sell system: Well depth, brand and hp of pump, jet or submersible pump, size of pressure tank, standard or variable speed pump system, date the current system was installed, pressure settings (at what pressure does the well pump start and stop?), line size, draw down rate of the well. Hopefully, there is a sticker or paper somewhere near your well with the name of the company that did the installation - they should have records either under the name of the home's previous owner or the property location.

8. Your well could be short-cycling for a variety of reasons: The pressure switch could be failing. The pump could be failing. The check valves or foot valve (if present) could have failed. There could be a hole in the line underground The pressure tank bladder could have failed. Taking pictures of the system as a whole, including tanks, valves, switches, controllers, etc will help us to help you diagnose the problem.