Hello!
About having to make absolutely everything from scratch for a Jam, I have no idea about rules like that, and being sincere, I've never tried to participate in one. But I suspect it's possible that they require that you write them instead of just importing or copy/pasting, so you use your own variable and method names and/or structure. I want to think in a similar way as in a programming exam. I'd like to see an answer here of people that had been in Jams and in a similar situation to let us know properly.
About your second question, about a place where you can find scripts that resolve a good bunch of things, made by the community... well... I think I've already offered a link before about that... the Unity wiki, if you browse a bit you will find very interesting things in it.
Again, the link to the main page:
http://wiki.unity3d.com/index.php/Main_Page
And a few places linked in it:
https://github.com/Unity-Technologies
http://wiki.unity3d.com/index.php/Scripts
If you even need more, you can check the Unity Store for free assets or GitHub, where a lot of developers like to show their work and offer it to the community (consider always the creator's work and effort of course).
For example, in my case, a while ago I made a map generator with TileMaps, and I used the Unity 2d extension for tilemaps, so I was able very easily to have animated tiles instead of static ones. Or in another example, in a prototype I started I created a dialogue/event generator but I wanted to have a visual tool to easily navigate through the dialogue branches and interact with the actions fired by the options. So I started to make my own node map, connectors and all the stuff, but then I discover xNode and I tried it and the result was more satisfactory that what I had implemented by the time.
Let us know if those links offer what you're looking for.
Cheers!