Hello, I created a squad with four pets and everything, and I put them on the battlefield, and got them researching... Later, when they were finished, I went back to the battlefield, but nothing had changed... except for the fact that it said I had no squads. 

Now I can't do anything with these pets. I want to change it back to a normal group, but it says I have to take them off the battlefield, and when I go back to the battlefield it says I don't have any squads. Please help me make this a normal group again and fix this!

You need to switch to Mirror instance. There's Homeworld instance on the screenshot.

Okay, but it still won't let me leave...

You need to land them on the Mirror first, before you can recall the squad. 
(It used to be possible to recall them during research, but for whatever reason, that got changed recently.)

Zaltys, it's still possible to remove the squad from the mirror instance while it is researching or after this when it's possible to land. Nothing has changed here. Could you please describe the conditions when your squad was unable to do this?

Basically, all the icons except research are greyed out while the squad is researching. 

For instance, my squad Arcanum (http://beastkeeper.com/pet/122537) is now ready to land on Mirror. Everything is greyed out, and their current status is listed as 'On Battlefield'. There seems to be no way to recall them. 

...I'll leave the squad like that, so you can take a look at it.

Thank you, we're investigating this issue. There's really something wrong with it.

Update: the problem must be fixed now. Sorry for the inconvenience.