Hi Rick,
Great job taking the initiative in trying to fill this information gap at a (unfortunately) commonly overlooked disorder. It's good to know that you are pushing out some quality content on the web. Now, let's talk about SEO.
Before you make ANY changes I would strongly urge you to first check out your web analytics and get a good grasp of your inbound traffic. You'll need to create some advanced segments and do some deep dive analysis to address some important questions...
- What percentage of your organic traffic is coming from branded keywords? Non-branded?
- What are your top 10 pages? Bottom 10 pages?
- What (inbound) keywords are driving traffic to each of your top 10 pages?
- Do the inbound keywords match your target keywords for that page?
- What are the rankings for your inbound keywords? For your target keywords?
- Do your inbound keywords have any search demand? Check the Google Adwords Keyword Tool.
- What keywords have the highest bounce rate and what page did they land on?
- Why do you think they bounced? Did the landing page match the keyword intent?
- Etc.
Essentially, what you are doing with this in-depth analysis is to determine what you already do well in and where you can improve. Your website is already live for 6+ months so you don't want to lose any traffic for something you already have traction in. From there, you can make a smart data-driven decision on what pages need to have their title tags changed, add on-page copy, what new videos/content you should create, etc.
As for your question about the video categorization, I would keep the videos under Noah's Minute and sub-categorize them. The main reason is NoahsDad.com is associated with the name Noah's Minute and in essence brands your website. Maybe you can even ask your existing followers to see if they are okay with this?
Regarding mis-spellings, I do not think that is a good idea. If you want to portray your website as an authoritative source to not just search engines but users as well, everything should be written correctly. Search engines can auto-correct mis-spellings so you don't have to worry about that. Here is an example for "downe syndrom videos".
Lastly, ranking for highly competitive keywords is never impossible - you just need to create extremely valuable content and gains lots of links to them. For example, you can create a category for "down syndrome facts and information". Push out some high quality content that includes some myth busting then link to your Noah's Minute subcategory videos and you'll start building out a robust internal link structure. From there, any incoming link equity would boost up your entire website.
At any rate, I hope this gives you a good head start on where to look first but there is a TON of other things we still haven't covered. I apologize in advance if some parts don't make sense but please don't hesitate to ask if you have questions.
Good luck! =]