Bitcoin transactions and blocks can be easily delivered using existing satellites.
There is no need to deliver special satellites for this purpose.
That is not the point, and no, existing satellites may not have the capabilities to serve as a full node and their operators are not people who would want to.
The specs are not that high though. According to this[1] post they use an ARM with 4 GB RAM and a 100GB SSD. Not sure about the predictions, but 100 GB does not sound like that satellite will still be up in 10 years.
[1]
https://groups.google.com/forum/#!topic/bitsat-project/2WFNsrcGhLs