"alte Freundin" means a female long-term friend. If she is an ex-partner, you would say "eine Exfreundin" or less harsh "jemand, mit der ich einmal zusammen war" ;) On the other hand, if you are not in a relationship anymore but still friends, "eine alte Freundin" (with the same meaning as above) is fine. If she is literally of old age, you do not mention that (it's rude) and just say "eine Freundin" or if you are in a relationship "meine Freundin".
Not really. At least not standing alone like this. It's really hard to explain the different connotations of switching word order in German, so I'm sorry if I can't give you a good explanation why that would not work, but if you put the "nur" at the front, it would mean something like "But I want a beer" - "... before I go" or "Thank you, ... , not a glass of wine like you just brought me" (told you it's complicated)
So what would the difference be between "eine ehemalige Freundin" and "eine alte Freundin"? For some reason, I had it in my head that the "alt" adjective could only describe something with respect to age and if you wanted to express the actual change of state of something (e.g. she was my girlfriend but isn't anymore) you use "ehemalige."