Is this expected that civiHR removes lots of features (eg activities and cases)?
(Note: My comments are focused mostly on CiviHR &lt;=1.4; for 1.5+, I haven't followed as closely.)

CiviHR is broken down into several different extensions. Each extension defines a different piece of the data-model/UI (eg for tracking job contracts or tracking qualifications). If you pick and choose these individually, it should be possible to load them onto a CiviCRM site without disabling/removing features.

One extension, org.civicrm.hrui, is particularly opinionated and aggressive about reworking the UI. Its primary purpose is to reshape the overall user-experience for standalone CiviHR deployments -- emphasizing HR-specific elements, de-emphasizing fundraising-specific elements, tweaking phrases/word-choices. It fills a role similar to Drupal's installation profiles.

If you're an experienced Civi implementer/consultant looking to add some HR elements to an existing Civi site, then you've probably used most of the same tricks as hrui (eg toggling components and toggling display preferences), and you'll probably disagree with some of the opinions in hrui. So skip it; you're not the target audience for that extension. Browse the list of extensions and pick the ones which are relevant.