So the Marston Vale Line is the last remnant of the old Varsity Line between Oxford and Cambridge. The line no longer exists between Bedford and Cambridge.
Interchange with the WCML is at Bletchley, the next stop south from Milton Keynes. Fun fact, Bletchley Park was chosen for its wartime role precisely because of its location on the railway halfway between Oxford and Cambridge.
EWR are upgrading the Marston Vale line, and the Oxford to Bletchley line, as well as building a new Bedford-Cambridge line to effectively restore the lost Varsity Line. Unfortunately, Bedford to Cambridge has been built upon in too many key locations, though frustratingly a lot of the alignment does still exist, just not enough.
The project already had a strong business case, but Universal has only strengthened it more. You'll probably find that the trains that will serve the completed route will be longer than they would have been, that would be my guess at least. This all depends on how much of the park traffic is expected to use this route.
Eurostar cannot run on the MML due to gauging. Eurostar trains are built to the European loading gauge (trains are taller and slightly wider) whilst the MML was not. Unfortunately, being the first country to build railways properly, we adopted a slightly smaller loading gauge (not talking track gauge) and kind of stuck to it. This is incidentally why you see double-deck trains on the continent, but not here.
The MML also simply has no capacity to take a Eurostar train. Those commuter Thameslink paths are far too valuable and heavily utilised. Additionally, given the cancellation of the HS2 eastern arm, the MML fast trains (your Nottinghams and your Sheffields) will not be moved to HS2 now, and will remain onnthe MML.