Multi-select is your only option at the moment. But extra fields will become more extendable in the coming versions.

Not as things are right now. Keep in mind that lots of things are being improved in K2 currently so this may change very soon.

The only way to add any functionality that is not available out-of-the-box is by creating a K2 plugin. If you feel confident with writing plugins for Joomla, you can check out the example plugin we have here: github.com/getk2/k2-example-plugin

You'll easily see that it's dead-simple to create your own set of fields using Joomla or K2 XML fields and then insert these into the K2 item edit form.