Ad 1) Yes, that should be feasible.
Ad 2) Basically, there is a railway line between Vienna and Salzburg, Austria's busiest line, which unfortunately does not run through mountainous areas. The landscape nonetheless is nice at most times, sometimes interrupted by a tunnel. If you want to go through mountainous areas, then you need to perform a relatively large detour via Semmering, Bruck an der Mur, Selzthal and Bischofshofen. Railway services in Austria are basically provided by ÖBB (www.oebb.at), between Vienna and Salzburg there is a second (private) operator, namely WESTBahn (www.westbahn.at), running trains once an hour.
TorontoHarold, I will provide more details tomorrow.
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