'Lithuanians' were a political grouping, not a linguistic grouping, the 'language' follows from the politics, not vice-versa.
They were in fact both. And the language does not always follow the politics - had this been the general rule, then entire Belarus and Lithuania should be speaking the same language, since both regions were part of the same policy for a very long time. Instead, "political Lithuanians" spoke at least several distinct languages - including Belarusian, Polish, Lithuanian and Yiddish.
Moreover, Lithuanians in Prussia were actually never part of "political Lithuanians" - since no part of that area ever under direct sovereignity of Lithuanian rulers in period between 1422 (the Treaty of Melno, which defined the north-western border of Lithuania for the next 500 years) and 1918.
Ethno-linguistic transformations (such as the switch from one language to another) - though greatly influenced by political, cultural and religious changes - often take place quite independently from the latter three, and not always follow them.
That was particularly true in the Grand Duchy of Lithuania, where Baltic Lithuanian language failed to dominate and instead at first Ruthenian (Old Belarusian) and then Polish became - next to Latin - the two official languages of the state. As the result Lithuanian language was rooted out almost completely from many areas (such as the Vilna Region) and replaced by Slavic languages (either Ruthenian or Polish, or at first by Ruthenian and then by Polish), while in other areas (such as the Kovno Governorate) Lithuanian survived almost exclusively among peasants and some part of petty nobles (the latter was the case especially in Samogitia).
For example in the Vilna County - which encompassed the countryside and small towns around the city of Vilna (but not the city itself) - according to the 1909 Russian census Lithuanian-speakers were only 7,2% of the total population, while 71,4% were Polish-speaking and Belarusian-speaking Roman Catholics, and the remaining 21,4% were Orthodox Christians (Slavic-speaking, mostly Belarusian-speakers) and Jews. In the city of Vilnius the proportion was even less favourable, with only 4,7% of the population being Lithuanian-speakers in 1909. Wileńszczyzna region had only negligible Lithuanian population by the end of the 19th century. The only controversy was whether its population was more Polish or more "Russian", since according to Russian propaganda, there were a lot of "Russian Catholics", who were allegedly not Poles. In reality most of the region was already Polish-speaking, but even East Slavic Belarusian-speaking Catholics identified as Poles, as opposed Orthodox Belarusian-speakers who usually didn't.
In entire Vilna Governorate according to 1897 census 59,6% of the population were Roman Catholics - of whom only 17,8% were Lithuanian-speakers and 41,8% were Slavic-speakers (Polish or Russian - including Great Russian, Little Russian and White Russian). According to 1909 census 60,7% of the population were Roman Catholics - of whom only 13,6% were Lithuanian-speakers and 47,1% were Slavic-speakers.
In the Kovno Governorate in 1897 among the total population 68,6% were agricultural population (peasants), but among Lithuanian-speakers - 85,4%. Lithuanian-speakers were 66,0% of the total population of this Governorate, but 82,2% among agricultural population.
As far as we know 'Baltia' was a continuum just like Slavia and Romancia were (even in the early modern era).
And Germania too, by the way. However, all of them were continuums of stair type - some boundaries were sharper than others. AFAIK you are not a professional linguist and neither am I, but I have read quite a lot about this and I know that for example Slovene language was very distinct from Old Church Slavonic already in the 10th century, when the Freising mnauscripts (in Old Slovene) were written.
Professional linguists can define approximate boundaries between languages, and within those languages also smaller sub-divisions can be identified - namely dialects and jargons (jargons being sub-divisions of dialects, and dialects of languages).
West Baltic languages were distinct from East Baltic languages. Today a popular theory is that there was never a Common Baltic language (which later diversified into West and East branches - as was thought in the past), but that West Baltic and East Baltic split directly from Balto-Slavic, and independently from each.
Surviving texts in Old Prussian language show that it was considerably different from Lithuanian. The two were certainly not mutually intelligible, given that probably even various Prussian dialects were not mutually intelligible - at least in the 16th century that was the case (for example we find information that Albrecht Hohenzollern ordered to translate Catechism to Old Prussians, and later he ordered to publish 2nd edition in another Prussian dialect, because not all Prussians could fully understand the 1st edition). But it is possible that various Prussian dialects became more diversified from each other after the conquest and Christianization, under the result of influence of foreign languages (for example, many loanwords from Polish can be seen in surviving Old Prussian texts).
Not sure you are right there.
Lithuanian immigration to East Prussia is well attested in sources of all kinds.
The eastern part of East Prussia (the borderland between the Grand Duchy of Lithuania and the State of the Teutonic Order) from the late 13th to the first half of the 15th centuries was very sparsely populated, heavily forested, and was known as "Grosse Wildnis" ("Great Wilderness").
That area was a frequent battlefield between the Teutonic Order and Pagan Lithuanian raiders. Therefore the Teutonic Order evacuated most of the remaining Old Prussian population from that region and resettled them to provinces located farther west. Only some people, living forest lifestyle remained there, but agricultural population was largely evacuated and fields were abandoned - that's how the region became "Grosse Wildnis".
Only later, when the devastating wars ended, the area started to be repopulated. Already in the 15th century spontaneous influx of Lithuanian settlers from the east started, and in the 16th century Duke Albrecht Hohenzollern invited more Lithuanians to settle in his lands, to help rebuild the war-devastated economy.
As the result Lithuanian immigrants moved in and the North-Eastern part of Prussia became known as "Klein Litauen" ("Lithuania Minor").
Of course those Lithuanians who moved in assimilated any groups of Old Prussian population that they encountered on their own. Those local Old Prussian groups - however - were very few in numbers, because the area was sparsely populated and largely deprived of large settlements and of permnanent agriculture.
That said, many Old Prussians from areas located farther west also participated in colonization of "Great Wilderness" - so Old Prussian settlers coming from the west would encounter Lithuanian settlers coming from the east, and the two groups would colonize the area together (in addition there was also influx of Polish settlers from the south, plus some Germans as well).
Anyway - it is right to say that the area was Lithuanized by Lithuanian immigration, combined - of course - with assimilation (Lithuanization) of some Prussians.