Hi there,
Sounds like an interesting project! I will try to answer the second question first, how I see this.
On the homepage you'd see a list of recent notes, then you could sort the nodes by quality, temperature and other factors, and search the nodes. Once you find a node you were looking for, you can open it up and from there see it's parent nodes, attach new nodes to it of type you want, or rate other nodes.
Visually, I imagine this pretty much like a forum/discussion board, with addition of that each node has it's type, can be rated, sorted...we could use breadcrumbs to depict users location and allow easy traversing in the node tree.
1) I would code it in PHP/MySQL (codeigniter framework), which is OOP/HMVC php framework, JavScript (jQuery), Bootstrap 3 for a nice and responsive UI. Clean code with inline documentation.
I'm happy to do the full user authentication as part of the first stage as I already have the auth lib I'm re using in all apps so this would actually be faster than writing a primitive one.
Looking forward to working with you!
Regards,
Julijan