TBH I don't think that there is an 100% foolproof way of knowing what CMS a website uses. I tested a few that I know what they are with http://whatcms.org/ and it seemed pretty good at detecting both WordPress and Drupal, but not so good at Joomla. Out of interest I also randomly tested some of the ones listed from the link you gave and it was pretty good at detecting WordPress but not so good at detecting the other 2 (claimed that no CMS was detected)... But as they state there is no foolproof way to check, unless you of course know for sure...

Regardless though, I personally I don't see any reason to doubt their claims about the example websites they suggest for each CMS. Maybe I'm just the trusting type but I see no reason why they would lie about it, there is no advantage to them and all 3 'major' CMS' would have a heaps of great looking sites online so it wouldn't be hard for them to legitimately compile such a list... Although I guess the info could be outdated? (I.e. some of them may have changed to another CMS since publishing that list).

As to your further questions about templates, you can't know that either... Nor what plugins/extensions/modules they use, whether they are free or paid, or whether they are default or custom...

Unfortunately you're going to need to do the hard yards yourself and in my experience, unless you have a plan for a really simple site, regardless of which you choose you will hit problems and issues and need to decide the best way forward.

If you google something like "drupal wordpress joomla comparison chart" you will literally find thousands of posts detailing the differences. But bottom line is that there is no "best CMS", only the one you prefer, or the one you decide is best for the job at hand...

My overall observations/opinions are as follows:

Learning Curve (from flattest -> steepest; i.e. easiest -> hardest)
WordPress -> Joomla -> Drupal.

Most flexible (i.e. can bend it to do what you want, assuming lots of dev knowledge or willingness to learn; from most -> least)
Drupal -> Joomla -> WordPress.

Modules/Plugins/Extensions and Templates/Themes available (from most -> least)
WordPress -> Drupal -> Joomla.

Free Modules/Plugins/Extensions and Templates/Themes available (from most -> least)
Drupal -> WordPress -> Joomla.

Personally I like Drupal best and even with a fairly basic php/html/css knowledge I didn't find it that hard to work with (I have done a few sites). But I know Joomla devs and they rave about it and love it. Likewise I know of a couple of total newbs who admin their own WordPress sites and are very happy...

So to answer your more indirect question/statement; my suggestion is for you to first flesh out what you actually want to do and how you intend to achieve it. If you are looking to produce a website that is wholly about videos (sort of like a 'youtube') then perhaps a generalist CMS isn't a good choice? (I'm not saying that it mightn't be, just throwing that thought out there...). Perhaps something like Kaltura might be a better option? Or maybe you just want to host your vids on youtube but have them agregated and displayed on your site, then a CMS might be a better option...?

Also I think that you need to assess what your current ability is, and how much you are willing to stretch it to achieve your ends... I.e. how much you want to learn. Perhaps you might be keen to learn lots, then maybe rather than a prebuild CMS, perhaps you'd rather create your own webapp, in which case you'll want a framework (rather than a CMS).

Personally I think once you can get clear about what it is that you are doing and how far you want to take it, download and install some TurnKey appliances, install them as VMs and have a play around... IMO it's only then that you can start to get a clearer idea of of the best way to achieve your plans...

You can use guess.scritch.org/ for checking the CMS or fremeworks of these sites. However, it is difficult to know exactly about the templates they are using.

As long as you are saying that they templates and designs looks professionals. It is not possbile freely, because each given website is customized to look like professional.