How to keep several local copies of a theme in sync?

as for your first answer , Like always, you can do that in many ways..
you can

• use a local folder synch

• write a function to allow wp to use a themefrom other install (3 filters to check : template_directory_uri // theme_root //theme_root_uri )

• install a multiblog network mode and use the same theme for all.

IMHO the best would be to to use local folder synch…

for your second answer , In my experience (and it is very individual) all frameworks / empty themes / blank files only complicate the work (unless you know them very good )
It is always better to start from scratch (depending on your level of course )
The only time I tried to use an empty / blank “framework” it took me 4 times as much time to develop the site than it usually does … but like I said, it is personal , and also depends on the complexity of your design or site (the more complex, the faster you should drop the idea of “frameworks”