To get schema changes on the server, just use South. If you change a table, it may have data, make sure that you record both the migration of the schema and, if necessary, the migration of data in order to preserve the meaning of your data.
In order to return my updated data to you (which does not seem critical, but it may be nice to work with current test data as it develops), I usually just use Django tools and dumpdates and loaddata commands. It's simple enough to dump the fixture and pass it to your repo, and then loaddata at your end.
You can try using git hooks to automate some of them, but if you want to automate, I recommend trying something like Fabric. Most of this stuff should not be triggered every time you push / pull (in particular, I usually don't want to unload a new data binding often).
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