Is it possible to repack an .apk to install it in an incompatible Android version? ('there is a problem parsing the package'/have 4.0.4-requires 4.1)
Short answer: No.

Simple repacking cannot solve the compatibility problem. If an app requires "at least Android XX", that usually means it needs some conditions not met before it. There are new OS features introduced with each Android version, libraries get additional APIs/features, etc. – nothing of that can be solved by "repacking" the installation package. If the (required) functionality cannot be provided by the Android version your device is running, the app cannot work (correctly) – even if you were able to install it.