Thank you

Grumbler, ARE YOU GOING to call _ my phone or SHALL WE use Google Hangouts?

why WE? Why not
Are you going to call to my phone or [are you going to] use google hangouts?

This person wants to communicate with you, but is wondering whether they should call your phone, or if you BOTH should meet on Google Hangouts and just message EACH OTHER.

BOTH - EACH OTHER - PLURAL —> WE

Also CALL MY PHONE (without TO)

Also WILL here is too namby-pamby. Is it a suggestion, will you ever do it, whose idea is it?? GOING TO asks “What’s the plan?”

I accept 'going to' and 'my'
My point was that if googe hangouts is no different from Skype/Whatsupp/Viber etc., then a call via Hangouts is the same as a call to a mobile, i.e. no arrangements are needed to 'meet' there.
I dont' even understand what was the point in asking this.

Because hangouts is a messaging app - you go there and message each other like you and I are doing here.

And if you were using Skype or Whatsapp, you would ask “Are you going to call me my phone, or shall WE skype/use whatsapp? Because ONE person can make a call to your phone, but TWO or more people have to meet in a forum or app.

No, I would ask "Are you going to phone or Skype me"
Alternatives
to make a Skype call
to call via/on Skype

For Google Hangouts it would be "Are going to use GH to call/contact me"

👍🏼

Because hangouts is a messaging app

No, it's for voice calls as well.

And if the OP meant messaging, the question would be different.

As far as I know, GH is a messaging app. https://en.wikipedia.org/wiki/Google_Hangouts

But I guess it does more than that reading on...

I posted my translation as an option.