You can use a PostGIS database cluster and use Slony PostgreSQL product for replication ( http://slony.info/ ) You need a server operating sistem and hardware to make data available to the clients. For that amount of data I think you will need a server
Yes I have used in many many years ago. The spatial properties must be explicit in the data such as a distance column, a latitude column, a proximity column. So yes you can but it is not implicit. Really WEKA is just a a collection of data mining algorthmns http://www.ijcaonline.org/proceedings/icacact/number1/7970-1006 for an example.
It is a very important question especially for developing countries. Indeed, without addressing this question dream of SDI is difficult to realize.
I agree to Jose Gomez Castaño advice. But there is another issue of efficient retrieval after storage especially of raster i.e. satellite imagery which is usually in terabytes. People are working on it. Hope soon more efficient and economical if not totally free technologies would be surfaced. Please have a look on this paper:
Traditional RDBMS will give you hard time to store Big Data and analyze that data. NoSQL DBs like Mongo DB will give you good performance for Big Data storage issues.