Ok
Once you have made you group (see above)
When you log in, click Start - Private Group this will then list all the groups that you are a member of, if not, then you have no groups- see above post on how to make & join groups.
If you want to wing up in game (this works for groups and open play)- I assume you have the default keybind layout for chat (aka you did not change it).
Press no.2 this will open up the chat box on the top left- but it will go to local (by default), then press ESC - This will take it off local tab, then press E or Q this makes the top tab move along the tab bar. This is a convoluted system, and ED know about it.
If you are off the LOCAL tab, then pressing no.2 again will open it up to where you had it last.
If your mate is a friend then it's easy, assuming he is in the private group, not solo. Move to the 2nd tob (friends) and select him (fire trigger or space is default)
This should offer you a few options- Text, wing invite, and voice coms.
Select WING INVITE, press space and this will send him/ her a wing invite - so you can group up together and help each other kill stuff.
He has to accept this for you to join up as a wing, and talk / write to each other. I think the error message you getting is a bit weird- maybe because he is in solo and you are in open #Idontknow.
Once you are in a wing together, you can simply press ENTER, to send a wing text to each other.
Also remember when you wing up together, the in game voice coms will automatically turn on (its cool but a bit slow vs TS, and some people don't like the sound it makes).
To turn off voice coms (remember its an open mic) see the pic below.
Press NO.2, press ESC, navigate along to the tab bar to the cog wheel on the far right, press space, and move the highlighted text to
auto enable voice coms, click it off- IF YOU WANT COMS OFF
I hope this helps you out
Fly safe, wing up and talk to each other (if you want)