Why "well" is here?

What does "geofencing" mean? Could you give me some examples?

"Geofencing" is a technological term. A "Geofence" is a virtual boundary or parameter for a real-world geographic location. So when a device exits or enters a "geofence", there could be different alerts, adverts, or other things sent to your advice. Other people may not know your exact location, but they can track you in relation to these geofences. Ex: When I got to the mall, I received an email from my favourite store there. Ex: Some countries use geofencing via BlueTooth to track COVID-19 cases. Ex: Geofencing improves marketing. Ex: I went to orientation at my university today and received so many alerts about textbooks for sale. They have efficient geofencing.

If I say "just not myself" instead of "just not me", would it change the meaning of the sentence?

"Just not [me/him/her/them/you]" is an expression used to mean that one is doing something that is out of character, that one is being unlike themselves. Thus, the meaning changes when you use "myself" instead of "me." Ex: You're so angry today. It's just not [like] you. Ex: This just isn't me. I don't think I'm being true to myself.

Why "well" is here?

"Well" in this case, is an exclamation used either as a pause to think of the next words or as a way to express agreement. Ex: The food, well, was delicious. Ex: Well, that sounds like a great idea!

Is it okay to say "based" instead of "grounded"?

Yes, you are absolutely right. "Based" can be used instead of "grounded" here. Ex: This research is science-based. Ex: We have scientifically-grounded research to prove our claims.

What does "fall apart" mean? Is it a common expression?

"Fall apart" is a common phrase! It has a couple of meanings. It either means something comes apart or disintegrates, or it means losing one's ability to cope emotionally. Here they're using it to refer to emotions! Ex: I fell apart when they played the last song at the wedding. = I cried when they played the last song at the wedding. Ex: Jane's gonna fall apart soon. = Jane's gonna have an emotional breakdown soon.