You can't change the docroot of a domain at the moment since domain management is turned off due to the DNS integration not being finished. What domain needs its docroot changed, and what should be the doc root for that domain?
As for the other questions:
1. Sqlite databases are just a file, there's no server component, so you should be able to use it assuming your node app contains/has access to a sqlite library for working with those files. If there's something that needs to be installed server side for it, Krydos may be able to install it.
2. No. You need a VPS for that.