Sounds like you have a good plan. Be present for the survey if possible and ask the surveyor lots of questions. Good surveyors are a wealth of information.
Get familiar with your chartplotter on the shakedown (if present) and check if there are up to date charts aboard. Are the instruments working, especially the depth sounder?
The surveyor should check the VHF but a radio check can't hurt.
Motor for no less than an hour. Take her up to cruising speed for a while. Back her down a 1,000 RPM's and cruise for a while. Try different speeds. Listen and feel what the engine is doing. At the end of an hour is she doing anything different, is she dropping revs? If she is the most likely culprit is dirty fuel or filters. Write down the filter numbers and buy spares.
After a couple of hours on the water go below and look for any signs of leaks from hatches and stanchions.
Backup fuel filters are a must and it would be best to start with a clean one.
Check on drip of the packing gland when the boat is idleing at the dock...and in gear underway.
Does it have a chartplotter?
You probably wont even use the radar, but make sure its operable
The advice above on the engine is very important and correct.
Check on the raw water impeller to see when it was last replaced and have at least 2 spares.
Check both manual and electric bilge pumps water entering ilge
Check for where the emrgency rudder handle is and that it fits
Check the rigging to make sure all pins are in and turnbuckles ok
Check on anchor, chain and make sure rode is secured to boat. See if
there is a backup anchor.
Check on pressuried water system
Does it have an burners/oven, check on propane/ solenoid switch if it does
Find out how much battery power ( types and how configured) ( 2 group 31 house bank and 1 group 24 starter. Check to make sure they have good water levels and are charged.
As far as a heater underway, desiel heaters are expensive add on add require venting. Usually they are permanent installations like dickensens etc
You can buy an expensive propane one ( we have the one below) which lasts about 5 hours on 1 1 lb bomb. We crack our cabin for ventilation which is enough. When we are anchored and its cold ( spring and fall) its plenty of heat for the boat.
We have a larger Coleman one no longer made which has a fan, but heats well
Coleman BlackCat Instastart PerfecTemp Catalytic Heater ? Walmart.com
Also these are advertised
Mr. Heater Portable Buddy Heater: Heating, Cooling, & Air Quality : Walmart.com