Which apps/services needs to be whitelisted when using AFWall+ firewall? I installed this root firewall app on my android but now some services are not working properly. For example, I liberated full access to Google play store on it and also Google play services but when I try to install an App in Play Store, it never starts the download. When I disable firewall, the downloads run normally.
You likely blocked the downloads by not whitelisting com.android.providers.downloads
From Question 58 of app FAQ

What do I need to do to get Google Play Store to work?
You need to whitelist the following: com.google.android.gms (Google Play Services for authorization) + com.android.providers.downloads (For Downloads) + com.android.vending (this is the Play Store)

(Emphasis Supplied)