1. Does strategic rail move have to be along friendly-controlled railroads (i.e. a railroads conncected to a friendly-controlled resource or objective hex).
The rule for Strategic Rail Movement says:
SPs moved by rail may move an unlimited distance through contiguous rail hexes. All hexes in the railroad line must be free of enemy SPs, outside the ZOI of enemy units, and all Towns along the railroad line must be friendly controlled.
It says quite a bit, but forgot to indicate the key point -- the rail line must be friendly controlled (6.5). I will mark this for amendment.
2. Can strategic rail move cross enemy-controlled navigable rivers?
The obvious answers are "yes" and "no", i.e. the same restrictions as regular rail moves, but as far as I can see, the rules are not clear on this.
No. 5.4.3 already covers this. Also, Rail Ferries are covered by 5.4.4.