I agree with Aequitarum's analysis. Just a couple additional points:
The engine is shared code for all of the processes, so I'm assuming that can be a shared assembly?
That seems reasonable.
If a shared assembly is in the same solution as a project that consumes it, how does it get consumed if it's supposed to be in the GAC?
Magic.
OK, its not magic. Let's suppose that in your solution your process project has a reference to the engine project. When you build the solution, you'll produce a project assembly that has a reference to the engine assembly. Visual Studio then copies the various files to the right directories. When you execute the process assembly, the runtime loader knows to look in the current directory for the engine assembly. If it cannot find it there, it looks in the global assembly cache. (This is a highly simplified view of loading policy; the real policy is considerably more complex than that.)
Stuff in the GAC should be truly global code; code that you reasonably expect large numbers of disparate projects to use.
Does that mean the engine.dll has to be reployed on every build?
I'm not sure what you mean by "redeployed". Like I said, if you have a project-to-project reference, the build system will automatically copy the files around to the right places.
the principle reason we separated the filter from the process (only one process uses it) is so that we can deploy the filter independently from the process so that the process executable doesn't need to be updated
I question whether that's actually valuable. Scenario one: no filter assembly, all filter code is in project.exe. You wish to update the filter code; you update project.exe. Scenario two: filter.dll, project.exe. You wish to update the filter code; you update filter.dll. How is scenario two cheaper or easier than scenario one? In both scenarios you're updating a file; why does it matter what the name of the file is?
However, perhaps it really is cheaper and easier for your particular scenario. The key thing to understand about assemblies is assemblies are the smallest unit of independently versionable and redistributable code. If you have two things and it makes sense to version and ship them independently of each other, then they should be in different assemblies; if it does not make sense to do that, then they should be in the same assembly.
I've read that assemblies link to specific versions of other assemblies, so if I update the DLL only, it's actually considered tampering. How can I update the DLL without changing the EXE? Is that what a publisher policy is for?
An assembly may be given a "strong name". When you name your assembly Foo.DLL, and you write Bar.EXE to say "Bar.EXE depends on Foo.DLL", then the runtime will load anything that happens to be named Foo.DLL; file names are not strong. If an evil hacker gets their own version of Foo.DLL onto the client machine, the loader will load it. A strong name lets Bar.EXE say "Bar.exe version 1.2 written by Bar Corporation depends on Foo.DLL version 1.4 written by Foo Corporation", and all the verifications are done against the cryptographically strong keys associated with Foo Corp and Bar Corp.
So yes, an assembly may be configured to bind only against a specific version from a specific company, to prevent tampering. What you can do to update an assembly to use a newer version is create a little XML file that tells the loader "you know how I said I wanted Foo.DLL v1.4? Well, actually if 1.5 is available, its OK to use that too."
What should I look for? I see lots of books about C# and .NET, but none about deployment or building or testing or things not related to the language itself.
Deployment is frequently neglected in books, I agree.
I would start by searching for "ClickOnce" if you're interested in deployment of managed Windows applications.