"app not installed" Replace ROM-based app with modified APK without root
INSTALL_FAILED_UPDATE_INCOMPATIBLE should tell you something. "app is already provided in stock Rom", "not rooted" and "I uninstalled it" don't match: w/o root, you cannot have uninstalled a system app (you probably have disabled it).

Same goes for Playstore: you cannot simply "update" it with a patched version. If it's an official version (signed by Google), you could update it – but then you must tell adb install you want to update: adb install -r xx.apk (note the -r, which stands for "re-install"). Not sure whether that works via adb for pre-installed apps, though (I've never tried).