I need a simple way to share texts, links to frameworks, videos and, of course, actual project data with multiple people. Things that come to mind are blog, wiki and public Facebook page. I also presume there is some software that could be used for this. Multiple people should be allowed to share. When someone shares/posts, he should be able to write a short description and the link. Being able to add some keywords/categories that could be used for searching would be nice, but it's not a must. The idea is to have a basic knowledge database that is searchable and available to all instead of hoarding it all on one computer.
Have you tried trello?
It's good for project management and also for sharing information.
We can narrow down your question to
how to share information?. The fact this piece of information has been found over the internet or somewhere else doesn't matter (as long as the source is properly documented).
Based on it, I believe you already know the answer... that's the basic idea of a Wiki. The most important thing here, however, is not to have a common place to share information... but to ensure the available information is up to date. That's discussed in another TOPIC.
Within the wiki, you can keep the tree structure you want, adding keywords for faster searching, add comments, keep track of page's history, copy / paste volatile content (from links that may get broken in the future) and a lot of things more.
So, in short:
Go for a Wiki.
Any of the basic collaboration tools/platforms out there should do the trick. This includes those hosted in the cloud as well as those you can install on your servers.
Google docs, wiki's, message boards, etc. All can do what you're looking for. Big differences will be in what kind of notifications and permissioning are available.
Start by finding out what kind of tools your team is used to using and pick the one that best fits in with their style (while still getting the job done).
How about some kind of microblogging services designed for collaborating with your team? Great example of it is Yammer (https://www.yammer.com/) which is very simple in use and should cover your expectations (at least I hope so, basing on what you've written here).
I have tried it in my team just because of curiosity (didn't really need that) and it seemed to be pretty useful.
We have an intrawiki that we use as an entire company for sharing information: We put contact information, instructions for various tasks, links to important information, etc. Departments and teams have their own sections on the intrawiki, and can even get as specific as information pertaining to small projects. Anyone can create and edit pages so it's easy for people to add their own information and update when necessary.
We use Confluence, which is not free: http://www.atlassian.com/software/confluence/overview
Media Wiki is also available: http://www.mediawiki.org/wiki/MediaWiki
I use Evernote and it works very well, easily sharing documents, videos, links, etc.. Everyone on my team uses it, and everything we share is available on all of our devices and computers.
I think that blog is the answer. We have two blogs within a company: technical and non-technical. Technical blog is great as it allows senior developers share their ideas, achievements in automation of our processes etc. It also encourages other developers to contribute. This works well in medium to large size organizations, as certain people tend to specialize in different areas. E.g. our system architect might write a blog on how our framework will change in the coming six months, when our quality assurance lead might give an insight on how quality assurance processes have improved within last few months.
Information can be shared, linked and easily accessible, but it doesn't mean that people will go and read it. It's just like going to Wikipedia - you go on it when you want to find something specific. If you want to encourage knowledge sharing within your organization, then blog might work better.
Another option would be Socialcast, which is designed for Intranet-based social networking. This is good for link sharing. If you want longer-term knowledge capture, I agree with an earlier poster who suggested putting up a Wiki.