I need help downloading "Google Play Services" on my Amazon Fire 7. I already managed to do "Google Play Store" and "Google Maps". Thank you!

By default - out of the box , you can't Google Play is not supported on Amazon Devices, you are restricted to the Amazon app store. BUT you can hack it - checkout this link
How to Get Google Play on Kindle Fire and Install Any Android App You Want

If you need further help, reach me via phone at https://www.6ya.com/expert/michael_e7c2c48c6e65f808

https://www.howtogeek.com/232726/how-to-install-the-google-play-store-on-your-amazon-fire-tablet/

you can use the silk browser, search for the play store and download it.

you need to root your device
http://www.howtogeek.com/232726/how-to-install-the-google-play-store-on-your-amazon-fire-tablet/

You can not. amazon has its own app store and proprietary os

If you need to install Google play on your Kindle Fire HD, root your Kindle Fire device at first. However, you can't root it like other Android device with one click rooting tool - iRoot, Framaroot, Kingo Root... The rooting process may be a little complicated while it's effective and safe.
For more detailed instruction, please refer to: http://www.iroot.com/how-to-articles/how-to-root-kindle-fire.html

Afterwards, install the Google play. Open run.bat. Choose option 6 and install it.

That is the thing, to use any, and I mean any Google app on Android you must have Google Play Services install.There are a variety of Google Play Services that you could download and install, but since your device is not an known brand to the Google Play Services, you need to download each version and try it, until you get the right one.
If you go to the link, you'll notice that it says "All Versions". When you read the version number, the last three numbers is the code to the device it is compatible with; example: the version that ends in 438, this version is compatible with Nexus 5.
Here is the link to download Google Play Services. Make sure that Unknown Sources is enable within Settings>Security.

http://www.apkmirror.com/apk/google-inc/google-play-services/

If you need to install Google play on your Kindle Fire HD, root your Kindle Fire device at first. However, you can't root it like other Android device with one click rooting tool - iRoot, Framaroot, Kingo Root... The rooting process may be a little complicated while it's effective and safe.
For more detailed instruction, please refer to:http://www.iroot.com/how-to-articles/how-to-root-kindle-fire.html

Afterwards, install the Google play. Open run.bat. Choose option 6 and install it.

Google Play Store 5 0 38 APK Download APKMirror