I believe the Trophy had an oil cooler as well; it was only necessary on the full-fairing models, but some people like to add it to the naked so they don't run as warm as they're supposed to.

It bolts straight on, like so many other parts from this series.
You obviously have a Speed Triple tail section, but again, bolt-on.
As far as the frame goes, you have a Speed Triple / Sprint / Daytona / Trophy / Trident frame. The differences in the models were determined by what was bolted onto the frame, not the frame itself.
I haven't gotten around to my Trident rebuild yet, but I picked up some used Honda CBR600 clip-ons from whenever it was they used 43mm forks on that model. I need to grind off a small lug on each, but they will fit nicely after that. Not nearly as nice as Roden's Tommasellis, but at US$30 not nearly as pricey either! Also, with a longer bolt, they'll take the factory bar-ends.
Also, your VIN, MOT, & reg are all very, very wrong. VIN should begin with "SMT" for a Hinckley bike. 1987 was 3 years after the Meriden factory was demolished & 3 years before the first Hinckley bike was sold.
Also, welcome!
Cheers,
-Kit