You ask, "Does the association allow the yard to be fenced?". The answer is no, and they have the power to do that because you are not buying the land, just the building. Because they own the land, they make the rules and can pretty well tell you what you can and can't do. Likely YOU will also have to "pass" their scrutiny and although you may have no issues with that, whoever you ultimately choose to SELL the unit to--some time in the future--will also have to go through their character checks. Often this step makes a unit harder to sell when you are ready.
And although the home appears to be a house, it is factory built and stands on a minimal foundation of cement blocks, and would be considered by most a double-wide trailer.
I am not a big fan of these mobile home parks for consumers. In general they are huge, and they tend to have a large population of children. I am leaning toward mischief issues here, and think you should call the local police and ask if that is or has been an issue.
You will be paying your mortgage of roughly $700, plus insurance, plus city, county and state property taxes, and then another $385 per month land rent to the "park operators". I would say that your budget will need to be $1,500 to $1,600 per month before you buy heat, electricity, phone, cable etc, etc.
If you are willing to spend that kind of money, my advice is to look a little further and you will find older homes on their own land, or newish condos that are solidly built that may even include garages.