Using libraries/APIs

I want to develop a desktop calendar app which syncs with Google Calendar.
Can I use this library/API in Xojo directly?

You could use direct web APIs via HTTPSocket classes.

For using Objective C, you could use declares or write a plugin.

I’m new to GUI programming,
So can I import ANY widget control available in Cocoa, inside Xojo, by simply declaring them?

No. For controls to work right they need to be subclasses and included with a plugin.

So what kind of things am I able to import using declare without using plugins?
I’m a medical student trying to learn programming as a hobby and self amusement, and plan to develop free and open-source apps for Mac OS X, thus I can’t afford plugins, is there any way to write my own plugins using something other than C languages?
For example I’m fluent in Ruby (although only used it to write console programs)

You can use plugin SDK to make your own plugin.
Like in this video:

With declares you can call C functions in a library.