FDW to postGIS Database

Let say that I have a database named stp. I also have another database
named geo that is a PostGIS database for storing geopolitical and
geospatial data. I want to set up a foreign data wrapper in stp to
connect to geo, so that for each address in stp, I only have to store
the primary key value of the lowest level geo unit, such as a city. I
can always display the city's county, state, country, whatever in views
in stp. I plan to have other databases that need geo data so I want a
single source of truth for geopolitical and geospatial data.

My questions are:
1. Do I have to install PostGIS in stp?....or is it sufficient to
install PostGIS only in geo?
2. Do I need the postgis extension in stp? (I'm thinking yes, but I
don't want to guess.)
3. I want to geocode addresses in stp. Do I need to install any
geocoding software in stp?...or can it be used from geo?

Thanks for your help!

Sue

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Susan E Hurst
Email: susan(dot)hurst(at)brookhurstdata(dot)com
Mobile: 314-486-3261