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I have replied to you questions regarding box beam barriers below in red. 

1)     This system appears to be common in New York and Wyoming. Do you know the status of this system as far as MASH compliance?

Box beam guardrail has been evaluated to MASH TL-3. Previous MASH full-scale crash testing was conducted on the G3 box beam guardrail system and New York’s box beam terminal design found that box beam systems with top mounting heights of 27 in. (685.6 mm) were capable of safely redirecting 2270P vehicles under TL-3 impact conditions.

With respect to the 1100C vehicles, recent cable barrier testing with S3x5.7 posts have shown a potential for laceration and penetration of the vehicle floorboard by the free edges of the post. According to MASH, this is sufficient cause for failure of the test based on penetration of the occupant compartment. To the best of our knowledge, this has not been evaluated through MASH testing of box beam with the 1100C vehicle.

http://mwrsf.unl.edu/researchhub/files/Report60/TRP-03-203-10-Vol1.pdf

http://mwrsf.unl.edu/researchhub/files/Report60/TRP-03-203-10-Vol2.pdf

http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w157.pdf

2) Should and can this system be raised to reflect the increased height of other barrier systems and if so how high?

Box beam median systems were evaluated under NCHRP Report no. 350 with small car vehicles at 28” top mounting heights. Without further analysis, it would be difficult to recommend heights above this even though the potential for them to perform adequately exists

3) 
Can this system be used with an inlet or post socket instead of a soil plate when continuing over a structure?

Because box beam is a weak post guardrail system, the main resistive force and energy absorption is derived from yielding and deformation of the post. Weak post systems typically depend much less on displacement of the post through soil. As such, cable barrier systems commonly have substituted sockets in place of deeper embedment posts or soil plates and demonstrated similar behavior. In terms of box beam guardrail, there is some potential that the use of as socketed foundation could alter post deformation and deflection slightly, and we have not observed this practice used box beam in any past crash tests. However, based on the performance of cable barrier systems with sockets, it would seem that the performance of a socketed post box beam system would be very similar to a standard system with posts and soil plates.