Is deactivating modules safe regarding settings?
It's impossible to say from here. Theoretically yes.
It depends on the module - a specific module could easily clear its variables in hook_disable(), or hook_uninstall(), or not at all. You'll have to check the install file for each module you disable to see how it will affect what you're doing. 


It sounds very much like you have two copies of the image_desaturate_formatter module in your Drupal install though; that could account for the error.

Regarding server logs - your host should give you access to these (I've never come across a host that would deny you access to your own logs, it's criminal!) so give them a call, they might have valuable information in them.