There is a lot to tackle in this question, but I'll help to answer this question by using the example of the Frankish people, since this is a group I am more familiar with (there are very, very many different groups of people who begin to occupy the Roman empire in late antiquity, so this question is quite broad as a result).

By the 4th and 5th centuries, the Frankish people were fairly well integrated into the Roman empire, likely as foederati (a group of people co-opted into the Roman military, in exchange for settlement within the empire). We also get a sense that as foederati, the Franks were still allowed their own independent legal framework while residing within the Roman empire, and as a result they would have still kept kings, who would have as a result acted as Roman officers within the Roman system. An early example of this is with King Mallobaudes, who himself served as an officer in the Roman army. We know that the Franks kept their own laws, which were codified under Clovis I in the late fifth/early sixth century (referred to as the Lex Salica). It is written in Latin (for the most part, some manuscripts contain glosses in the germanic vernacular, Fronconian) and has some instances of Roman influence, however is likely based on an older tradition (The Oxford Dictionary of Late Antiquity refers to the Lex Salica as one of the least Roman-influenced of the Germanic laws of Late Antiquity).

We know that, at least from a sixth century reference in Agathias' History, the Franks were quite well kept:

'Their hair is never cut from childhood on, and hangs down in abundance on their shoulders. Their front hair is part on the forehead and falls down on either side. Their hair is not uncombed and dry and dirty and braided up in a messy knot like that of the Turks and Avars; instead, they anoint it with unguents of different sorts, and carefully comb it.' (this is speaking of the nobles, as Agathias later cites that lower-class individuals kept their hair 'cut all round'). (This translation is found in Cameron's article, 'How did the Merovingian Kings wear their hair?').

I'm not sure if we have any direct early mentions of the clothes which the Franks would have worn, however almost definitely they would have been wearing woven clothing, likely some sort of tunic. This (I'll admit slightly dated) account of what Germanic iron-age peoples were wearing can be found in Owen's The Germanic People: 'The men are now wearing long-sleeved jackets which reach almost to the knees; the woolen or skin mantle held at the neck by a brooch or safety pin is, however, much the same, but trousers have now made their appearance. This sartorial custom was taken over from the Celts, who in turn had it from the Eastern European, or Asiatic horsemen of the steppes.' He also goes on to talk about that these people were typically weaving clothing, at least out of materials like wool and linen, which would have also been dyed.

So for the most part, the idea of the 'savage caveman' overcoming the Roman empire is not factual. These were people who were civilized in their own right. I can't speak to written language or scientific ventures, but they would have certainly had their own customs, laws, beliefs (mind you, most Germanic peoples convert to Christianity quite early), etc.