Welcome to Just Answer !.
I hold questions open after positive ratings to allow for unlimited follow up.
Please be patient though. The research & typing take time.
I will discuss each of the topics you brought up briefly.. then if you wish we can get into more detail later.
You can generally shut off 30% of a heating systems registers without causing the furnace to over heat.
If it has air conditioning the system might ice the coil if you shut off more than 25 or 30% of the registers...as long as it runs and doesn't ice it will be OK....be sure to keep a clean air filter in it if you begin shutting down registers.
When you shut off registers, the ones you do not shut off simply move more air.. .. if the thermostat is located in one of the rooms that you leave the registers open in.. then you will still get reasonable temperature control.
Regarding the weather-wall unit installed in the 1970's... generally speaking, any money other than service or repairs costing less than $200 is possibly worth while... over that, especially repairs costing $500 or $1,000 or more repair is not a good idea.
Heat pumps of that vintage are complex, with parts hard to find... when a system sticks in cooling mode and will not go into heat mode it can be something as simple as a bad coil on the 4 way reversing valve (cost to replace $25-- $350) ... or a mechanically stuck reversing valve, cost to repair $600- $800.
It can also be problems with some of the other components generally costing $500 or so because of the diagnostics involved.... a heat pump that old is past due for most of its major components to fail... think twice about spending any money on it... it is worth a service call to diagnose however.
Those old heat pumps are 50 to 60% less efficient than the average modern heat pump... it could easily pay for itself within 4 or 5 years on energy savings.
Let me know what your annual utility bills are per year and I can assess that for you,
You can save money on heating by using mattress warmers between the inner springs and box springs of the mattresses, and setting the thermostats 5 or 10 degrees cooler at night.
Look this information over, let me know what you think... we can go from there until you have all of the information you need. There are no time limits.
I will be in for another hour or two tonight, then back in the morning, west coast USA time.