dvr

That's not true Ivylog. Some of the DVR's might require an add-on OTA tuner but they certainly can receive OTA programming.

Your Dish DVR is not going to have a OTA tuner. Some DVD recorders have the necessary tuner.

Look on the back of the receiver. If there is a 2nd coax input (not output) labeled OTA or similar wording then yes, if you connect an coax from your OTA antenna you will be able to record and they will show up in the program guide.

Yes, if your Dish receiver is equipped to receive OTA stations.