You've actually asked about 3 questions in one. So I'll try to separate them out and answer each one.
1.) If the program you want to keep was recorded on your old DVR, you cannot transfer it onto the new DVR. Your options are to either watch it during the 30-day transition period, or use a device (such as a DVD recorder) to record the program off the DVR in real time.
2.) If the program you want to keep is an On Demand purchase, this program is stored on Verizon servers and linked to your account. You won't lose it when you return your old DVR.
3.) To transfer recording schedules, favorite channels and various other settings, you will need to use the DVR > Settings > Export Series to Cloud function (note: if you live in an IMG 1.9.1 area, you may only save your recording schedules). Then use the Import function on your new DVR (in 1.9.1 areas there is no import function, if you are not prompted to import during setup, try setting up a new series recording of one of your current series to force an import prompt).
Hope this helps.