Theodor Mommsen (the guy who wrote a very influential history of Rome) used to be a casual antisemite but once Treitschke and Marr started calling for a genocide he instead wrote "Auch ein Wort über unsere Juden" which regarded all the Jews in Europe as one of the German tribes, footing to their Yiddish language. That was part of the Antisemitismusstreit and happened in the end of the 19th century. Nietzsche also would take part in that "strife", attacking the antisemites on racial grounds. There were Jewish intellectuals as well who would appeal, to no avail, to a German nationhood of all the Jews. Chaim Zhitlovsky wrote letters to Hitler in the belief he could convince him that the Jews are German. That was not a success. The essentialist brand of German nationalism has been conservative (and thus antisemitic) from the days it appeared in the Napoleonic era.

Heinrich Heine (the poet) used to be a member of a German nationalist student fraternity (a Burschenschaft) in 1820 but in 1821 he would get thrown of the Goettingen university because he fought a duel against someone who accused him of secretly still being a Jew (which would have barred him from studying). He was also booted from his fraternity because they already formally barred any Jews from taking part during the Burschentag in 1820. Heine didn't deem it important to mention he converted from Judaism upon joining them. In his book on Ludwig Börne he described his Burschenschaft like this:

With what petty finickiness and pickiness they discussed the distinguishing marks of German nationality! Where does the Teuton begin? Where does he end? May a German smoke tobacco? No, claimed the majority. May a German wear gloves? Yes, but only of buffalo hide. (The dirty Massmann wanted to be on the safe side and did not wear any.) But drinking beer is permitted to a German, and he should do it as a genuine son of Germania, for Tacitus speaks quite precisely of German cerevisia.

In the beer cellar at Göttingen I used to have to admire the thoroughness with which my Old German friends created their proscription lists for the day when they would come to power. Whoever descended in the seventh generation from a Frenchman, Jew, or Slav was to be condemned to exile. Whoever had written the least thing against, say, Jahn or any Old German absurdities could prepare himself for death, specifically death by the ax, not the guillotine, even though this was originally a German invention and already known in the Middle Ages under the name of the “Welsche Falle.” I remember in this connection that they quite seriously debated whether a certain Berlin writer, who in the first volume of his work had spoken out against the art of gymnastics, should already be put on the above-mentioned proscription list, for the last volume of his book had not yet appeared, and in this last volume the author might perhaps say things that would give a quite different significance to the incriminated utterances of the first volume.

The Burschenschafter pioneered the current Belgian and German flags (Black, Red, Golden). In 1817 they have celebrated the first German translation of the bible on the Wartburg fest by burning books deemed too foreign or too liberal. Of course there also were liberal nationalists.

During the Hambacher Fest of 1832 the exiled liberal Ludwig Börne got celebrated as "the great German writer" explicitly because to the Burschenschafter he was not a German but, like Heine, "Jewish" instead. Like Heine he at first was more conservative but the conservatives didn't want him because they've been antisemites. The anti-Jewish laws got repelled together with Feudal laws by the French and were associated with the old regime.

Were there any Jewish German nationalists, who felt a strong connection to their home country and wanted to make it stronger?

You're asking if all Jews are trators or not now? For real?