1) aren't we supposed to have a FULLY functioning remote?
Yes, at least more operational than just the mute button. Incidently, the mute, volume up and volume down buttons only affect the Slingplayer client. It doesn't actually control the set-top box.
2) aren't we supposed to be able to choose what to watch from our recorded shows?
Yes. The most common issue with controlling DirecTV boxes, is that they have two features that might conflict with the Slingbox's ability to control them.
First feature is that each DirecTV box has an option to use either an Radio Frequency (RF) or Infra Red (IR) remote. The Slingbox only has IR Blasters, so it cannot control the box if it is currently set to RF. Check the DirecTV setup menu to see if your set-top box and remote are set to IR or RF.
The other issue is remote address pairing. This allows multiple DirecTV boxes to exist in the same area, but each box will only respond to the paired remote control. The IR codes provided by Sling Media presumes the Slingbox will be controlling a box with the address #1. Check the DirecTV setup menu to see if your set-top box and remote are set to a different address.
If the DirecTV box is using IR and set to address #1, then you should check the IR blasters if they are functioning properly. The following article (http://support.slingbox.com/get/KB-5000042.html) will help you determine if they are operational.