Is there a way to have a language neutral link that automatically redirects to the user's active language?
I'm not familiar with the "slider" module. But from the example URLs you added, it seems to me that at least you should check your configuration at Configuration -> Languages -> detection and selection: the order specified there should be 'URL, Default, User', and not something like 'Default, URL, User'. It could well be that that is all that's needed here ...

Curious to hear what the result of checking this will be ...