If #1 is associated with just that one particular speaker output from the receiver, than I fear it's a problem internal to the receiver.
The DSP is the Digital Signal Processor -- it's the engine that applies the various sound processing features to the audio -- sound equalization in your room and decompressing the various digital DD and DTS audio formats, for example. I doubt that updating its code would make any difference to this problem.
#2 is most likely a problem in the HDMI/HDCP protocol -- the language that the devices use to send status and command packets to one another. In principle, it should be fixable by updating firmware in all of the devices -- in your DirectTV box, in the receiver and in your TV. A bug in any of them can affect all of them since HDMI/HDCP is a bi-directional protocol.
Marantz SR7009 avr + MM9000 amp --> Atmos 7.1.4
Fronts=NHT 2.9+AC2, FH+TM=DefTech PM1000, LCR+TM amped