Sorry if it sounds a dumb question but I always thought using the official playstore that comes pre-installed is the safest so everything related to F-Droid is new to me. Did anyone had apprehension on installing F-Droid when you had bare to none knowledge how it works? I like to be cautious and on the page it has a Instructions to verify the download page and it only tells how to check from Linux but not from Android, what am I missing here?
You don’t need to verify it. Download it and then temporarily turn on install from unknown sources. Once F-droid is installed you can turn off the install from unknown sources setting. When you first install an app from F-droid you will need to grant F-droid permission to install apps.
I personally I think F-droid is far better than the Play store. I don’t even use the Play store on my device as I don’t use or install Google services. I run pure Lineage OS with only apps from F-droid. F-droid takes a strong stance on freedom, libre software and privacy. To be on F-droid you need to meet strict requirements.