How to find downloaded .apk files on my Android phone I usually download apps and games from Google Play but I wonder if i could reuse these files and find them again if my application has been removed?
Please help. Thank you in advance.
There are a bunch of apps to backup the .apk file of apps from your device, making the process much easier than fiddling with file explorers. I e.g. used AppMonster quite a while; its paid version even automatically captures the .apk of each app when it's installed or updated. Looks like the app is discontinued – but there are several similar apps you can find listed behind the first link.

Once you've got the .apk, you can of course side-load it to another device if needed. I've usually done that if I needed the same app on another device which didn't have Playstore access. Note that this doesn't always work with paid apps: if those use Google's license check, the "target device" needs to be setup with the same Google account the app was acquired, and of course needs the Playstore app and network access to verify the license.

Of course you can use the .apk to reinstall the app even if it was removed from Playstore. License check should work fine then as well (provided you've got the Playstore app and your account setup, as described in the previous paragraph).