Can I add new production Processes? If so, where do I do this? Also, can the production orders with these new processes show up in my cellar worksheet and/or brewer worksheet?
Yes. You can create a new process. For example, we have customers that do secondary fermentation, so they created "Green Primary" and "Green Secondary". Then, instead of using the prefix GB on their items, they use GP and GS.
Another example is that people have added the "Dry Spice" step, which they consider different than "Dry Hop" (basically, they aren't adding hops, they are adding a spice, so the term Dry Hop didn't make sense).
In that case, they created an item with prefix DS, and have it between the Green Beer and Bright Beer BOMs. Then you just create the items with the new prefix, and adjust the BOMs to include the new process.
To get the items to show up on the Cellar Sheet, Pack Sheet etc. you just need to set the Process Type on the item.
Dry Hopping, Filtration, Barrel Aging all show up on Cellar Sheet, so just assign the new items one of those, and it will show up in all the same places.