1. I think the $$/WAR number I see is from Fangraphs. It's a silly metric anyway, because every market is different - that said the Sox have a very high marginal value of victory - wins are a big boost financially for them, so they'd be on the high end of this in general.
2. The huge difference between bWAR and fWAR comes from the defense accounting - fWAR starts from FIP, bWAR from runs allowed. There are two competing assumptions at work here. First - bWAR is kind of starting with the pitcher getting a majority of the onus for runs allowed and works from there, fWAR starts from lower assignment of credit/blame. Second, fWAR assumes BABIP is entirely random - which is not true. Running the numbers today using 2015 qualified starters, there was a 0.43 correlation between BABIP and line drive rate. (in English, they rise and fall together, generally ... they are not independent, but they are not linearly related either) Last year Price had a 23% line drive rate, which put him in the bottom quartile and an outlier from his normal 20% or so rate (solidly above the median). So there is some cause for concern maybe - but right now, regression is the bet.
3. I wrote that entire #2 not realizing you (as I) misread the bbref entry. They gave him 2 lines (or 4 lines for the last 2 seasons) because he was dealt each of the last 2 seasons. His bWAR in 2015 was 6.0, and his bWAR in 2014 was 4.6 bWAR. Both are actually close to fWAR. 2013 his bWAR was 2.8. He also pitched about 40 innings less in 2013 than he did in 2015 (and 60 less than 2014!). 2014 and 2013 were two years where he had poor BABIP luck relative to other years in his career.