Yes, R&D verification that was inefficient, and probably led to massive overbuilding and wasted cost in the fabrication and construction of the assemblies involved with Apollo.
Massively computed FE makes things cheaper and safer. It would be lunacy to even think about doing hand calcs for a multi-million DOF dynamics problem. The analysts that do this work in various manufacturing fields certainly have the mathematics capability to do what was done during Apollo, but they do things better now by leveraging the tools at their disposal.
A great deal of what NASA and, specifically, the research labs that support it, use are proprietary, internal-only packages. For classified work, they can't share data with 3rd party developers for bug fixing, so they reinvent the wheel in-house. Much of that may be derived from open source packages like Salome, but you'll probably never find that information publicly.
The commercial contractors will all use major MCAD packages like CATIA, NX, Nastran, etc.
What do you mean you can get across Spain, France and Germany at speed (a pretty large area).
The US is more than six times bigger than these three countries combined. All of Western Europe is nowhere close to as big as the US. You have to think about building a connected rail system, from scratch, in an area the size of all of Europe, including Scandinavia, Eastern Europe, and parts of Russia. It can be done, but it's a humongous project.
"A complex system that works is invariably found to have evolved from a simple system that worked." -- John Gall, _Systemantics_