How to 'force' update apps? I am currently using Huawei's smart phone. The has KitKat installed and it is rooted.  

Huawei's app center shows that updates are available for a number of apps (not system) but the same apps updates are not available via Google Play Store.
I don't want to update my apps via App Center of Huawei.  

Is it possible to force Google Play to check for update and then update the apps? Any app available for that?
Some apps use the "staged rollout" feature of Google Play, which means that not all users get the update at the same time (I'm not entirely sure on exactly how it distributes the updates, but it does). So no, if the update is not shown in Google Play, the only way to get it is to wait.

However, APKMirror provides (some) APKs which you can manually install by downloading them onto your device and installing them 

Note that "Unknown sources" should not need to be enabled, as the majority of these APKs seem to be the original, signed APKs - that is, the APK's cryptographic signature guarantees that it is unmodified from the company. 

How does this work? I'm going to skim over the details, but essentially, the company that produces the app (for example, Google) has a secret "key" which they use to cryptographically sign the APK. Android checks that the new version of the APK is signed using the same key as the one that's installed (and that all the files within it match checksums provided by the APK), and if it doesn't (meaning that the APK has potentially been modified by some third party), it will refuse to install it.