I have downloaded an
.ipa file (a free game). when I trying to install it form iTunes to my device, it is stuck on installing:
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It is very uncommon to download / install a IPA file - free of charge or not.
The IPA files are usually used for known & registered devices (e.g. beta testers) - if your device is not registered and your device is not included in the IPA profile file, then installing the IPA file will fail.
This is kind of the Apple philosophy / protection: either you have a "deep" contact to the developer who includes your device (maximum is 200 devices as far as I know), or you jailbreak (?) your device, or you use the official AppStore and trash the IPA file.