Danny,
Couple of answers for you:
You can have multiple sde installations for different databases but yes, you can have only one SDEHOME at a time.
The version of PostgreSQL supported for 10sp3 is the same one as it was for 10.0, 8.3.8 with Postgis 1.5.3.
If you are using a Postgres version that we do not certify, than you run the risk of the Postgres client libraries being different enough from the ones found in the version that we do certify on, for our st_geometry dll/so to be inaccessible. In which case there is nothing that can be done. The only way to fix it would be for the st_geometry library to be recompiled with the newer Postgres client libraries and that ends up being a new release.
Sincerely,
Kasia