http://www.nintendo.com/consumer/wfc/en_na/ds/results.jsp?error_code=001-0105&system=3DS&locale=lang
http://www.nintendo.com/consumer/wfc/en_na/ds/results.jsp?error_code=001-0502&system=3DS&locale=lang
No worries, you haven't broke any rules, and sorry that you didn't receive a faster response for your problems.
According to Nintendo's Error Code Lookup, the 001-0502 really only indicates a possible eShop maintenance issue, so really that shouldn't be the issue since this has unfortunately been going on for a month and the eShop and/or their Online servers haven't had problems for that long of a time.
So really the 001-0105 is more helpful at explaining what the problem is, as it mentions something like wireless interference being the cause, which it does sound like that when you can connect sometimes and then at other times, can't.
So perhaps try checking for other electronics like cordless phones and perhaps either making sure that they are powered off or moved to another room and see if one or more might be the cause of your 3DS connection issue(s).
But if still no luck, perhaps you might want to give a call to Nintendo's 1-800-255-3700 (6 am ~ 7 pm Pacific, everyday) Customer Service number, and one of the service representatives can do some over the phone troubleshooting to determine exactly what the problem(s) might be, and then talk you through any needed steps to correct this.