The ability to group message with others relies on MMS rather than SMS. By using MMS, phones involved in the conversation are able to keep track not just of the original sender but also about everyone else involved. This is true for Windows Phone and I am quite sure for all other platforms as well.
Like you mentioned in your question, when you have a group ...
Since Messenger is being retired I doubt it.
Messenger is being merged with Skype, under the Skype name now. So you could download the Skype app.
Here is an email (dated January 10, 2013) I got from Microsoft:
We are retiring the existing Messenger service globally (except for
mainland China where Messenger will continue to be available) ...
I think that with Windows Phone 7, you don't need a special app for Windows Live Messenger chat, because this channel was integrated into OS.
You can go into Settings->email+accounts->add an account and add your Live account here (if it is not already there). And then you go into Messages and slide the pivot screen to the left or right. There you see your ...
The first tick indicates that the message has been delivered to the Facebook server.
The second tick indicates that the message has been delivered to the recipient's phone. It doesn't necessarily mean that the recipient has read it.
If the profile picture of the recipient appears, instead of the tick it means that the recipient has read your message.
AFAIK the best option would be Threema. This messaging tool is made by a swiss company supporting end-to-end encryption and no need for any personal data if you don't want. According to the company any data will be deleted from their servers as soon as a message was delivered. I haven't tried it myself yet but I heard some good things.
Do you have your Facebook account linked "properly" to your windows phone account?
You can still chat without it, but I wasn't receiving all messages, I'd be receiving some, I'd reply, but I wouldn't receive the message in reply to mine.
Once I linked them, it was working. To check if you have linked them properly:
Log into outlook.com
Go to Account ...
Looks like that version of Messenger is no longer supported on Windows Phone 8.1. Here's an official announcement from Facebook stating that various apps would be discontinued on older operating systems, including WP8 as well as older versions of iOS and Android:
Update on messaging support for older versions of Messenger and Facebook apps
Yes it is true that you can use messenger app without a facebook account but the WP app does not support that functionality. You may consider creating a facebook account. That's not a very big deal. Otherwise you can't use messenger
Facebook has developed its applications i.e. Facebook and Messenger differently for Windows Phone 8.x and Windows 10 Mobile. So you don't have to be worried about restrictions of W10M variant of Messenger while installing Messenger on a 8.1 device. I don't know whether it supports 520 or not as I never dealt with <1GB RAM devices but if 8.x variant does ...
As already mentioned, Live Messenger is on it's way out, and it's already integrated into WP7.5
However, there was a third-party Live Messenger app available before 7.5 came out, called "Messenger by Miyowa". I just checked, and it's still on the marketplace.