Ok, this one is quite tricky.
I've seen several times the word "old" placed so that it denotes the same as "former", or close so. But it'd never raised my eyebrows before, I've never had a thought about it, actually. Out of a quick research about it, I came to the conclusion that these two words can be considered synonyms, but it's important to point out that "former" is the option you'd pick up mostly in order to sound formal.
According to the Cambridge Dictionary, "old" is difined as "having lived or existed for many years". As you can see, this short definition (far be it from me to judge it!) indicates only a relative age of something (or someone), making it clear that the element qualified by the adjective HAS BEEN existing for a long time since its conception. Notice, however, that this defitinion doesn't imply the inexistence of the element at the moment. It has been being for a long time, but it still is!
As for "former", the definition is as follows: "of or in an earlier time; before the present time or in the past". Whatever it was, it clearly doesn't exist anymore. It's in the past and I can't even estimate the extent of the interval when this existed back in the past.
Check this sentence, so that you can identify the definitions above: "my old wife" (no,too rude, huh?), never mind. "My old house" could mean that my house is old or that I'm talking about the house I used to live in or that I owned. I could never say "this is former" as "former" is a classifying adjective and thefore it may be placed before a noun only. So, "former" means "ex".
I wouldn't worry about ancient, this is defined as very, very old, as in "ancient civilisations".
I've listed these words according to their very main meanings. Things can get a lot different sometimes...