Can we apply searches on the server?
Not currently, but this will be possible in the Adaptable Blotter Server Edition which is scheduled to be released in late 2019.
Can we ship the application to users with existing searches?
Yes. You can create as many 'predefined' Adaptable Blotter Objects as you require, including Advanced Searches.
Does Advanced Search update if I edit the data in the grid?
Yes it does. As soon as you make an edit the Adaptable Blotter will re-evaluate if that row should be visible or not and react accordingly.
Note that this is the default behaviour. You can change this to Never, or only after a ThrottleDelay by setting the filterActionOnUserDataChange property in Blotter Options. See Filter Options for more information.
Does Advanced Search update if the underlying data changes?
That depends on what you have specified for the filterActionOnExternalDataChange property in Blotter Options.
The default is Never meaning that it wont update as ticking data changes or the underlying data set changes. But you can change this to Always or after a ThrottleDelay. See Layout Options for more information.