As Alfredo wrote, one basic factor about GPL CMS systems is how big and active is the community grown around each one of them.

In this sense Wordpress, Joomla and Drupal are the ones I would consider.

Then, about how much SEO friendly they are, the first thing you have to know is that all of them have basic SEO features, but that for all them you have to implement new plugins, modules or components.

For instance, for Wordpress I would suggest the SEO plugin by Yoast, SEO Friendly Image and social sharing button (for instance Active Share by OrangeSoda)

Remember that Wordpress is a blogging system, even though it is possible to create more classic web sites with it too.

Joomla is interesting especially because of its community and the tons of devs that almost daily produce new plugins, modules and components for it. It is not so hard to learn too.

Its default SEO features are good, but it is better to install specific components that add more SEO functionality. The most popular are sh404SEF and JoomSEF, but I invite you to explore here to find other software you may need.

Drupal. Of the three is the hardest to learn, but many SEOs consider it best one. Regarding it I warmly suggest you to read this post on Search Engine Journal

Every content that is behind a login is not crawlable, therefore it won't be indexed by search engines. So, no, it is not necessary to SEO those content, even though a basic SEO should have to be done just because it is a way to have a clean site.

For instance, this Q&A will be totally crawlable in two weeks, when it will be visible to all the not PRO members, therefore not behind a login access.

Personally I have not seen any change actually. And reason is simple: the farmer update still is not alive in the regional Googles, as advised Matt Cutts in its post.

What would be interesting would be to see:

1. how the web farms affected in the Google.com ranks in the regional Googles? This can be especially interesting examining all the english based regional Googles (discounting the localization factors);
2. how big the difference in traffic will be when the algo update will affect also all the Googles, as - I suppose - then we will see its effects over all the translated/international versions of the websites, which are seriously vampirezed from local farmer sites.

If your site - I imagine - is targeting the French market, therefore Google.fr, therefore I believe you don't have seen any change yet simply because the farmer update still in not alive on regional Googles (as Google.fr is).

But mine is just an assumption, not knowing the real target (therefore Google version) of your site.

Not so easy to answer, because definitely we are not talking just about SEO, but essentially of Marketing and Brand Marketing. I will try to give you my opinion, also basing it on my 11 years of experience in Media industry.

The choice, as an SEO, would be to have one site, as all the backlinks, citations and social buzz would pointing to just one domain. Anyway, I would wisely design the different communication areas in order they seems visually (and psichologically) different for the user. In that way you can maintain the essential difference between the three media (Newspaper, Radio, Tv), also because - as you say about the Radio - these media not necessarely have the same main focus.

My main concern as an SEO would be the indexation of such a big website, therefore I would put all my attention on the navigational architecture of a site that would include all the three distinct ones.

BUT, as Marketer and if the branding between the three Medium is very different, I would not put them under the same domain, but I would mantain them separate and croslink them editorially (for instance the newspaper using videos of the tv site). This could also better the construction of your News Media Group enthity.

More over, using three different sites/domains it is possible to strategy web marketing plan which complement themselves, in order to conquer three different range of searches and users.

In this last case, the real problem wouldn't be SEO, but the coordination of the tree SEO/web marketing plans.

To make rest a project after a while. That pause will benefit your creativity, because your brain will work on it in the background without stress. When you return to the project, it will seems new somehow and those ideas your mind was breeding will come out with force.