Why can't Android device use Google service without permission? Now Google doesn't allow HuaWei to ship their services with the phone and the install-after-shipment route is blocked too. 

I think Google apps like Map/Gmail/Search/Youtube/Drive/Docs/Play/Assistant are all standard Android applications that can be installed on any Android compatible (no need to be certificated) devices.

Does the above fact means that Google's Android apps will use some DRM like mechanism to first verify whether the device is certificated or it won't run? If so, does this apply to all Google Android apps, or only some apps?
First the problem is mainly a legal problem, not a technical problem: Huawei is not allowed to install the Google apps.

Second the Google apps you mention are only the user visible part - similar to an iceberg there is a large hidden part you don't directly see:

The Google Play Services and it's, libraries. 

This is not a normal "app" as it is running as a system app and therefore can't be installed by a user. And it is required by each app you mentioned and even more. Most of the regular apps you find in Google Play Store also make use of this service, e.g. for receiving push notifications. Therefore the impact of not having Google apps pre-installed on a device is larger than you expect. 

And even if you manage to install the Google apps on a device Google will recognize that this device is not allowed to use Google apps: Every device and every firmware version is certified by Google. In that process Google creates some sort of fingerprint that allows to identify each device. 
As an end user you can ask Google for an exception for your device by registering it's Google Services Framework ID at Google. This will then allow you to use Google apps until you do a factory reset.