Alright I'll take a stab, at least at the first couple elements of your question.

Your assumption regarding 'SPQR Romans' is somewhat flawed. There was no transitionary point between the Western Roman Empire and the creation of the Holy Roman Empire. They were entirely separate entities, with over 300 years between the fall of the former and the rise of the latter.

Roman Soldiers (and im going to assume you are referring to the Western Roman Empire, as the Eastern Empire continued to thrive long after the West broke up) continued to think of themselves as exactly that - Roman Soldiers - up until Western Rome ceased to exist as an independent entity - sometime in the 5th Century AD.

While it is commonly noted that non-romans - specifically people of tribes who had migrated to the borders of the Empire - began to make up a larger portion of the Roman military at this time. However, often this would serve as a method of romanisation of said tribes, as much as it was 'barbarizing' the Roman military. All in all Roman military traditions were very hard to break down.

I'm not as familiar on the sword/technological changes, hopefully someone can come along and help out more with that. I do know that after the 2nd Century AD longer swords seem to have become more common, and in general infantry were known to start adapting more wargear from their cavalry counterparts, including helms and oval shields (as opposed to the rectangular scutum that I'm sure you're familiar with). This was a gradual transformation and during this time they would most definitely still have referred to themselves as Roman soldiers, though auxiliary troops (who made up around half of all troops during the height of the Empire) also identified by their home region, such as Batavia or Tungria.

Also, it should be noted that the "Roman" soldiers you're describing, with the equipment you mention, really only existed for a relatively short period of time during the 1st and maybe 2nd century AD. Prior to this Republican armies were far less standardised. The stereotypical Roman legionary that you are describing is exactly that - a stereotype that had been pointed to so much as to make it seem the norm, while it was anything but.

I would recommend reading up on Roman military after the crisis of the 3rd Century, when many of the stereotypes started to break down due to massive external and internal pressure. The armies of Diocletian, Constantine and others were really a far cry from the legionaries of the Pax Romana a century or more before.

Sources:

Bishop and Coulston, M.C. & J.C.N. (2006). Roman Military Equipment From the Punic Wars to the Fall of Rome

Cowan, Ross (2015). Roman Legionary, AD 284-337: The Age of Diocletian and Constantine the Great

Nicasie, M.J. (1998). Twilight of Empire: The Roman Army from the Reign of Diocletian until the Battle of Adrianople.

Adrian Goldsworthy (1998) The Roman Army at War 100 BC – AD 200

in what attempts have been made at defining when the Gladius morphed into some intermediate sword type before the Oakeshott Type X sword

It is still not really defined strictly, but many consider the Durostorum spatha (dated 278 to 313 AD) to be the birth of the migration era sword development that culminated with the type X.

and for how long (after the Fall of Western Rome to the germanic tribes) soldiers and officers still called themselves SPQR

Well, the usage of the term "Roman" obviously continued in various vague terms for centuries, but the Roman senate itself did not.

The senate continued to exist(and at times even have authority) under "barbarian" kings for some time, it did not disappear until pope Gregory the Great, sometime between 593 and 603, the senate ceased to be.

Source;

The Popes and the Papacy in the Early Middle Ages (Routledge Revivals): 476-752 By Jeffrey Richards, page 246