Heat Pumps and Electric Home Heating - questionable practice

here's my situation. i installed a new honeywell programmable rth7400d t-stat on a 96 goodman heatpump. the old t-stat was a janitrol mercury. it now seems that the fan continually runs even when the set temp is met. it blows warm till temp is met then turns off heat but fan continues to run. my old t-stat never ran this much. now for the questions...
1) is my heat pump running more effiecient with new t-stat eventhough is is almost always blowing some type of air? and has a very short off time between cycles?
2)should i use the programable t-stat like it says to with lowering the temp during the day and raising the temp in the morning and evening? will this save $?
3)should i go to a digital t-stat (non-programable) installed by hvac contractor for 199?
thank you!

had heat pump semi annual service done prior to t-stat problem. the company sent a guy out to clean ans service, he said the goodman heat pump was in good condition no low r-22 refrigerant level. another contractor from the company that came out to my house to fix t-stat (refer to previous post) said my r-22 level was low and put 71$ and 66$ worth in. should i be questioning this? am i getting hosed?

If he put freon in and didnt find a leak then you have a problem.