Is there a shop like Cydia on iOS for Android? Most apps in the Google Play store have a free version and a paid version. On iOS there is a shop called Cydia, where you can try out most apps for free before you buy them in the App Store.

Is there such a store for rooted Androids as well?

I know of the store F-Droid for free software


  F-Droid is an installable catalogue of FOSS (Free and Open Source Software)
While there are Android markets offering pirated versions, (not try before you buy which is signified usually by Demo or Lite) as the other users have mentioned, installing them is very risky. I would recommend being involved in the development community. As a developer I share keys and am invited to test apps often by frequenting XDA forums and Reddit.com/r/Android. 
Developers will discount or give away versions of their apps and being involved in the community will help you learn more and score you some software deals.

Update:This answer does not really address the question.