1.      "Capitalism is an economic theory."

That is essentially correct.

2.      "A Capitalist however, whilst being:

1. a person who has capital, esp. extensive capital, invested in business enterprises.
2. An investor of capital in business, especially one having a major financial interest in an important enterprise.
3. a person who invests capital in a business (especially a large business).

(the same definition from different sources)

or simply a person of great wealth,"

What about a Capitalist being a person who believes in capitalism as an economic theory. You seem to have fastened to the wealth end of the thing - to gain that wealth, the person was a capitalist and believed in the economic theory of capitalism and the opportunities it afforded them long before they became wealthy.

3.      "can also be,

1. a conservative advocate of capitalism (noun)
2. favoring or practicing capitalism [syn: capitalistic] [ant: socialist] (adjective)

... note the antonym ...

3. A supporter of capitalism.
4. an advocate of capitalism."
      
Note that that is conservative with a small "c", usually reserved for describing someone who tends not to like or trust change, especially sudden change. Now that is rather strange because if anything history has shown us that capitalism actually relies on and thrives on change. But I think the inference you wished to make and implant was the conservative with the capital "C". Politically, in the course of history there have been many extremely "Liberal" and "Radical" people who were quite successful capitalists, especially during the agricultural and industrial "revolutions" in Great Britain. Also looking back through the course of social and domestic history with 20 x 20 hindsight the "Luddites" were wrong, had their path been followed hundreds of thousands would have starved or been forced to flee the land and homes of their birth due to lack of food, lack of work and lack of opportunity.

Yes I did note the antonym and, strictly speaking, it is incorrect. That is not surprising considering you are using one of many definitions of the word capitalism from a dictionary. Dictionaries do not solely restrict themselves to what a particular word actually means, they also detail meanings of the word attributed to common or popular usage. Now how a word is used is different from what that word actually means and was originally coined to represent. Common usage may change over the passage of time, the original meaning of the word does not - best example I can think of to illustrate this would be the word "gay".

4.      "A supporter of capitalism will, as a matter of course, need to justify it in the context of politics and the political issues that surround it."

Why would a supporter of capitalism need to justify the application of that economic theory in the context of politics?? I am a firm believer in the economic strengths of capitalism purely because it works and that is all the justification it needs - there's nothing political about that whatsoever. So this requirement is just something that you have made up and injected into the discussion to suit where you wish to go as the remainder of your post shows:

"Any argument advanced in that context can be said to be a political argument.

A self proclaimed capitalist can therefore be said to be representative of a political ideology."

Which, for you, completes the loop you started out with when you introduced the word conservative.

Some definitions for you:

Communism - noun - The belief in a society without different classes in which the methods of production are owned and controlled by all its members and everyone works as much as they can and receives what they need.

Absolutely impossible to achieve, relies heavily on central control and as such cannot cope with sudden changes in response to extremely local circumstances. Immediately on setting this system up it corrupts itself as it has been seen to do down through the march of history. Very true analogy is that if two sailors abandon ship and find themselves in a rowing boat - One of them has to be the "Captain" or both will die - so much for equality. Particularly liked the bit of nonsense that "everybody works as much as they can and receives what they need" who decides?? The individual certainly cannot, otherwise nobody would work above the absolute bare minimum and remember you get out in direct proportion to what you put in.

Socialism - noun - The set of beliefs which states that all people are equal and should share equally in the wealth of the country, or the political systems based on these beliefs.

Left to concerning itself with politics of administration and handling of problems arising from conditions within the society it governs it is highly commendable, but all too often it meddles with economics where it shouldn't to make things equal which so blatantly are not and in so doing promotes a process of dumbing down, a reduction to the lowest common denominator, acting to destroy drive and innovation resulting in mediocrity.

Capitalism - noun - an economic system in which resources and means of production are privately owned and prices, production, and the distribution of goods are determined mainly by competition in a free market.

Provides the financial strength and flexibility to weather any storm and support any "political" system you may care for, but it does not alter the fact one jot that the economic system is completely separate from the political beliefs of the capitalist.