1) Probably would work best adding the inbound platform west of Moody St. crossing opposite the current platform, since that's the only place you can put a full-length platform and have trains not foul the Moody and Elm crossings at the same time. The current midblock platform is just too awkwardly short and would have to go. Would entail switching the angled parking to parallel parking, shifting the current platform back where the switch currently is so the DT can be extended, installing the other side platform abutting the Biagio Ristorante parking lot with back egresses onto the Charles River Greenway. Only tricky part is getting permission from Biagio's to have the platform egresses so close to their property. Any parking loss can easily be compensated when the midblock platform is abandoned; they can buff it out with a few more spaces of extra width.
2) Yep. And one of the main low-motivation points is that the decrepit Jackson and Newton St. overpasses need replacement. Kind of pointless to lay DT if MassDOT is eventually going to be on the ground doing lots of side abutment work for the replacements. Easier to wait till after they're done. It's also an ADA mini-high station, so they've got bigger fish to fry getting one or both of the non-accessible Belmont stops up to compliance first. All in due time.
3) No. Lowell is the clearance route that can do 17' tall, wide-load Plate F cars, and thus the only route PAR uses into Boston unless it's got a service disruption to work around (in which case Reading is #2). There is no freight whatsoever on the Fitchburg Line inbound of Willows, and hasn't been since the now-closed Ocean Spray plant in Littleton ended rail deliveries. Nothing's reached inbound of Littleton since the last Watertown Branch delivery almost 10 years ago. All Boston jobs originate out of Lawrence, not Ayer, so unless there's a reshuffle to some Ayer-Boston routings inner Fitchburg's strictly a tertiary backup route at this point. Even if it did see "a" freight job or two reshuffled to Ayer, you're talking very small rinky-dink stuff like Everett and Peabody. The biggest Boston-area job, PAR's DOBO to Boston Sand & Gravel, is forever captive to the Lowell Line because it originates in Dover, NH.
4) Correct. Not possible to trench because of the Charles, not possible to bridge because of the Jackson and Newton overpasses not allowing enough running room. Best they can do probably is grouping both platforms west of Moody so Elm stays un-fouled during train stops, optimizing the traffic signaling to dump the car queues quickly after a train, and maybe tarting up the alley between Moody and Elm a block south of the station as a quasi- River St. Extension to offer a cross-block load-bearing match to Carter St. on the other side of the tracks. There's definitely slack space today in that sub-optimal downtown street grid to tighten up the bolts beneficially. In no way is Waltham Ctr. the irredeemable dumpster fire that is downtown Framingham abutting those Worcester Line crossings. Waltham has good room for improvement with inexpensive finesse touches if they pick their spots carefully.