To take a quick shot at answering your questions...

BGCM and St. Maries River are both principally lumber haulers. St. Maries River has a healthy traffic base, mostly from the big Potlatch mill and a smaller stud mill in St. Maries. BGCM handles mostly lumber traffic, though not too many years ago there was some serious talk within the Williams organization about rebuilding what's left of the old Headquarters branch for log traffic.

Washington & Idaho handles mostly grain and lumber.

Boothill & Western has two locomotives on it, an Alco S-1 and a chopnosed GP-7 pr -9. The Geep does not appear to have moved in many years, it's visible in 2012 Google Streetview with the cab windows boarded up. The Alco is apparently the motive power of choice, around 2013 Google shows it at the grain elevator around the end of the active track 8 miles out of Dodge City, in the most recent image it's in the small fenced compound with the Geep in Dodge City.

Nevada Northern isn't on your list, its another car storage operation out of Shafter, Nevada. Power there is a GE 45-ton of mixed and various heritage, though it hasn't moved in a number of years now. They use a rubber tired loader with a coupler mounted on one end as needed.

Fremont Northern...a brief amount of internet searching shows Williams bought the line from the Nebraska railroad Museum (Fremont & Elkhorn Valley Railroad) in 2011, after the museum had their bank loan called. Williams promised to do a lot of track work to allow the museum to continue operating but never did, now it appears the museum is either gone or barely hanging on and is in the process of parceling out equipment. Also sounds like some of the track has been removed and at least some crossings either removed or paved over.

Jeff Moore
Elko, NV