Well, my girlfriend was using a lot skype for roleplaying with her best friend... But since some days, Skype seems to not launch anymore for both of them (on windows), so it seems it's time to move to a new software after all this time.
They were mentally prepared since Microsoft buy of skype, unfortunately, they're having a very hard time finding something to replace it, and now they have to find something. And I don't know a lot concerning this softwares, so I thought some of you may be could help us :)

What they need is :
- an instant messaging software (for text)
- which records discussions for at least 1 month
- Which permit to save the discussion as text (if possible which permit to export them)
- which permit to edit at least the last message to correct typos
- which isn't too "heavy" (old pc)
- which isn't too "modern/big-buttons/ugly-modern-interface-which-loose-so-much-space"
- which is free (& which is safe to use ;))
- if possible, which doesn't do auto-formatting ( = when *this* becomes automatically this).

They tried Discord : despite auto-formatting, could be very nice, unfortunately, they haven't found the way to export their sessions in text (you have to scroll through the whole discussion with endless scrolling and... it's really too much painful, they've long sessions).
They tried Pidgin : could be the perfect solution, but... you cannot edit you last message (which is an issue unfortunately :/).

Sorry for this long message and list !
If someone could help, that would be marvelous, and we would be really grateful :)

Try Tango.

Try Discord anyway and vote on an export function.
Also Discord now has a search function and bots that could probably take care of your issue.

Okay, but seriously...

I am also getting more and more annoyed at Skype but there are not that many that support Linux, Windows, OSX AND Android.

Just Google something like 'reddit skype alternative'.

I use Hangouts mostly and sometimes Whatsapp.

Viber, vine, Oovoo... Especially Oovoo is, mmmmm!

I like Jitsi, its Java, its not dependent on anything and runs on everything. Unfortunately you will probably need to expand its "STUN address list" manually.

I'm not sure if this is suitable for your needs but I used Mumble for gaming with some friends some time back. Free, multi-platform, excellent quality and low latency. You'll need a server though..

I use wire.
It's open source. The code is available on github.

No need to install anything, if you don't want to, as there is also a web interface.