Is there an elegant way to get data out of wikidata in a format that you can then fill back into another Wikibase without the pain of such conversions (like splitting coordinates, changing columns, changing the prefixes...)
Depends on how elegant you want it to be but it won't be trivial. If you want to get data from WDQS, you can use any of the available SPARQL text/regex manipulation functions to convert the WKT format into a different format.
Question 2 is related: When you extract dates with the QueryService that will change just years like 1971 from 1971-00-00 into 1971-01-01 dates. I felt unable to tell whether such a date was just a year or actually a January 1 entry. Is there a way to get the exact date as it has been put in to Wikibase back from the QueryService?
Again, this is not trivial. You need to also query the datePrecision field of the date value and that means querying for the actual date statement and not just the simple value that the usual SPARQL queries provide. Then based on the datePrecision value (I think 9 is for year precision vs. 11 for day precision), you can then truncate the date to just the year.