DMA & FIR Filter, some questions.

That's correct you shouldn't need to manually write any HDL. Once you are done verifying your filter using the DSP tools you can use the HDL for the filter and import it into component editor from within SOPC Builder. Component editor creates a .tcl file that describes your component with information like interfaces, signal direction/width, timing characteristics, etc... Once that .tcl file is created then your filter will show up in SOPC Builder just like any other component in there.

For something like this what I would do is after you have validated that the filter is working correctly use the same test vectors when you validate the entire system with the DMA and filter included. So you would populate the input vector into memory, trigger a DMA transfer, inspect the output vector that the DMA wrote out. You can use Nios II for this if the vectors are small enough to fit into main memory, otherwise you could use something like system console to populate the vectors in memory (and even trigger the DMA to operate since Nios II would be optional at that point).