Well welcome! You’ve certainly come to the right place. It’s great to have you. It looks like you’re decently along in your studies.
Be sure to check out The Ultimate Beginner meta-thread to get the lay of the land, and answers to some common questions. (The welcome link there will offer forum tips and how-tos). Feel free to open a thread if you have any questions (but definitely check in at that link to see if any threads have already been started on your topic.) Also, definitely take advantage of the search function (although it seems to only be returning results from posts made in just the last few days lately…that is, it doesn’t seem to be searching the whole forum, just posts within the last few days.) So don’t get discouraged if you aren’t getting many hits. If you don’t find what you’re looking for, feel free to PM me (or anyone else, I guess). We might be able to remember if (and where) a topic is. But I’m pretty sure most of the common ones are covered in that meta-thread.
Also don’t worry about bumping an old one if you want to re-open a subject. It’s usually better to do that, unless you have a very specific question and the older thread is really long. (They can get that way sometimes.)
You might find it surprising you were never introduced to these scholars in your studies, but sadly that’s not uncommon. As I was saying here and here, I know of university professors of economics…who have never even heard of Hayek. But of course, that’s basically the reason for the mission of the Mises Institute 
As for your piece here, you’ve done a pretty nice job. It’s actually kind of coincidental that you would post this now, as I actually just read a nice short description of the money concept from Tom Woods, which I just posted here.
I think you might actually want to include that link, or incorporate some of that language about how a money comes about. I think it will help your explanation by helping people grasp what money actually is and what it’s for.
You do a good job of covering a lot of bases. When you introduce a scenario, I instantly think of all the different hypotheticals someone might raise…but you quickly address them. (Not many people have the prescience to do this.)
One thing you don’t mention though, that I think would be useful is the relative ease with which transactions could take place today under a gold standard. How many cash-less transactions already take place everyday? People always raise the issue of gold being too cumbersome and heavy to carry around, or too valuable for practical everyday use (i.e. even a piece of gold as small as a gram is worth $50…and most everyday transactions require smaller denominations). But with today’s technology, you could easily have credit cards that simply account in gold. That way you could easily numerically divide the gold down as small as you want. In fact, Peter Schiff’s company Euro Pacific Bank actually offers such a card (although due to ridiculous regulations in the US it’s only available for non-US residents).
A bit later you state “Which option you choose depends on which activity will demand the least effort from your side – this is similar to saying which activity is profitable to you.” While there’s not anything technically wrong with that statement, you might consider rewording it, as it might lead someone to start thinking of profit in terms of effort. You might say something like “Which option you choose depends on which activity you are better suited to and/or are more interested in doing – this is similar to saying which activity is preferrable to you.”
Your fiat example reminded me of this post, which you might find useful to draw on for ideas. You might also get some use out of this one.
When you talk about where the name “dollar” came from, if you’re going to quote Rothbard, there’s no real need to basically paraphrase him right before you quote it. Either paraphrase it yourself, or just quote it. You might just say:
In fact, the term ‘dollar’ originated from coins which earned a reputation for their quality:
Murray Rothbard in his book, What Has Government Done to Our Money?: [the quote you used]
I’m not so sure I would use the premise of “redefining the dollar”. While correct in a technical sense, I think this will lose a lot of your audience. It is a bit difficult for a novice to follow, and is not really the most practical method, as simply dictating by fiat that a piece of paper is worth a certain amount is bad enough…but when it already has an established market value…and literally billions of people already hold them, there’s really no way to do such a thing.
The real solution is to simply remove more and more of the legal tender laws and the restrictions on currency, until you have a free market for money in which competition can exist freely. Competing currencies will develop their own values and, as you said, there will be a constant move toward a single money.
Finally, I would choose a more telling term than to say the gold standard was “abandoned” by government. “Abandoned” implies it was simply not good enough, or something better was developed. Obviously the reality is the gold standard was removed because it was restraining government growth, and powerful people both in government and special banking interests with ties to government needed a manipulatable money system to more easily maintain their dominance and grow their power. Of course The Creature from Jekyll Island is one of the best resources on this. (Others can be found here.)
I would say something more along the lines of the gold standard was “abolished” by private banking interests.
Minor corrections:
“Similary, a mining company will mine gold till the time it is profitable for it to do so.”…I think you mean unprofitable.
“each laborers” should be “each laborer”
Also, you might wish to hyperlink the title of Rothbard’s book directly to the text itself…either the document page with all the links to the text, or the wiki page (which also includes a link to the document page) or the HTML or PDF itself.
Other sources can be found here:
Overall you’ve got a pretty nice writeup here. I think if you look through the links provided here and incorporate some of those points, and provide the rest in a “resources” section or something like that for people interested in more information, you’ll have a great post.
Once again, welcome!