There's Sinatra for more barebones things, but honestly, homegrown solutions always grow into a shittier version of Rails. You don't have to use all of the features Rails provides. As others have mentioned, for simple APIs Sinatra is fine.
You kind of do. First, you have to opt-out, not opt-in. And the opt-out path is less battle-tested, so there's a lot of skeletons to be found there. Use it at your own risk.
If you want the best modern example of a ruby framework which starts small (like sinatra) but allows you to opt into a wider feature-set (like rails), you should give roda a look: https://www.youtube.com/watch?v=9fukis_VHl4
An old joke: any sufficiently advanced Sinatra app is indistinguishable from Rails.