Romania: Yes, Romanian is a language based on Vulgar Latin. Since High Middle Ages it has been subject to strong Slavic influence (it is argued that in XVI-XVII century up to 50% of the vocabulary was of Slavic origin) that led to the 're-latinization' since early 19th century [1], concurrent with the 'Romanian national awakening' that eventually resulted in proclamation of the Romanian state.

Hungary: Correct, just a small correction on the timeframe: Hungarians (or Magyars, to differentiate from modern citizens of Hungary many of whom are of e.g. Slavic origin) migrated southwest to modern Bashkiria and Perm region somewhere around 5th century AD. In the early 9th century AD they moved west, towards what is now Central Ukraine and entered the Carpathian Basin only in the last decade of 9th century.

Romani: That's about it. It can be also added that they came to Europe even earlier, quite possibly in 10th century, as they were mentioned in Byzantine sources from 11th century [2]. In 14th century they moved north, to modern Romania and west, to what is today Western Balkans and Northern Italy.

[1] Niculescu, A., Outline History of the Romanian Language. Bucharest 1981 [2] Fraser, A., The Gypsies, Wiley-Blackwell 1995

I can confirm what you cited for the Hungarians, but going further back gets a little hazy. The Magyars (which is what Hungarian's still call themselves and who they directly descend from culturally, although it should be noted that, genetically, contemporary Eastern Europeans are almost indistinguishable from each other) were one of many tribes who perhaps through cultural dominance or sheer population became the leader of a confederation of tribes migrating out of the Central Asian steppes. The reasons for the migration vary and are still in contention, but its generally accepted that pressure from further eastern Turkic steppe peoples (the Pechenegs who were pressured west by a confederation of Uzes, Oghuz, Kimeks, and Karluks, who in turn were pressured by Khazars and Cumans, et cetera) finally forced them west of the Dnieper River. There are numerous citations and descriptions from various secondary sources as to the appearance and disposition of these nomadic steppe tribes, but hard to differentiate with absolute certainty due to the size and diversity of the migrations.

Archaeology played somewhat of an important role, but as a nomadic tribe part of a much larger equestrian steppe culture with a penchant for oral tradition, unfortunately there is little to no written record remaining except from those secondary sources, and any archaeological record from before that time period is difficult to differentiate due to a wide ethno-diversity in the region with similar traditions. Also, it is speculated that the migration in and of itself cultivated a new cultural shift, which makes comparison of the old very difficult. There is, however, remnants of an Old Hungarian Script, a "runic" or "runiform", that was used until about the 17th Century, and had a small revival in the 20th Century, which is a child system of the Old Turkic Alphabet.

Linguistics on the other hand, a relatively newer branch of study, has afforded a slightly clearer perspective. Rather than having Scythian and such ancestry as was speculated for some time, it is now widely accepted that the Hungarian language is of the Uralic family, more specifically the Finno-Ugric grouping (in this case, the Ugric side) which shares relations with a few northern/eastern languages. Current linguistic development models date the formation of the language to at least 800BC, with various loan words and influencers, particularly of Turkic origin. This puts the Hungarian origin more-or-less in the region of the Ural Mountains in Russia, but which side they called their homeland is still speculative.

Anyway, that's about all I know off hand, sources available upon request.

You have the right idea although you have to remember it’s more about assimilation than ethnic mixing.

For example, the Romans and Dacians never mixed in the way you think. The Romans who migrated the Dacia assimilated the Dacians into their culture, making them speak Latin and follow Roman traditions. They managed to do this as the Romans had most of the power. The average Romanian today has very little if any Roman heritage.

Also it’s the same with Hungarians. Uralic Asians moved into Hungary and took it over, and assimilated the native population and made them speak Hungarian and follow Uralic traditions. The average Hungarians usually has extremely little if not no Asian blood in them.