Can you also say this with -ince somehow?
Sen gidince zaman bize haber ver, for example?
Or Sen gidince bize haber ver?
Your second sentence is correct. Gidince zaman... is wrong.
Gittiğinde bize haber ver.
Gittiğin zaman bize haber ver.
Gidince bize haber ver.
They all mean the same.
Thank you very much!
Why is "gittiğinizde" not accepted? Is that not the right form for siz?
it is accepted. You may have had a mistake somewhere else :)
Wouldn't "Gittiğinde haber ver" also make sense? I mean I always use this phrase without the "us", but that may be some sort of colloquialism too.
this is a correct sentence. But missing an information given in the English sentence, "us". "Gittiğinde haber ver" doesn't really tell whom he should let know
Can I form this sentence with "bilmek" instead of "haber vermek", for example "Gittiğinde bize bildirin" or does that change the sense?
It is totally fine (and was a forgotten alternative). It has been added. :)