Is it safe to give app permissions

Yes. The storage permission grants an app access to the whole “Internal SD Card”, where all your photos, musics, downloads reside . It’s usually safe to assume that apps you trust access only what they need, but a random unknown app may scan your files and expose some privacy problem.24 Eyl 2018

Storage permission is needed by apps that will read/write files onto the storage especially files accessible by the user .

These are the permission types to pay attention to when downloading a new app: