how do Hebrew-speaking Jews study Aramaic sections of the Torah original text?

Factual Questions
1

the original Hebrew text of the Book of Daniel is supposed to contain sections written in Aramaic rendered in Hebrew alphabet. So for Jews who wish to study the Torah in the original (probably some groups still do, and pretty much everybody did that just a few centuries ago in Eastern European Jewish communities), how do they handle reading this Aramaic? Is the Aramaic of Daniel sufficiently similar to Hebrew to be understandable as a messed-up dialect variant? Or do/did they just sort of memorize the meaning of the foreign language text based on a Hebrew translation so that it “makes sense” without really being able to read a larger set of similar Aramaic texts?

2

It’s read in the original Aramaic. Plenty of Hebrew prayers are also in Aramaic, including the Kaddish, perhaps the most commonly-spoked prayer of them all.

Biblical Aramaic is similar enough to biblical Hebrew (or modern Hebrew, for that matter, as they’re essentially the same language) for a Hebrew-speaker to understand it, although it’s a bit of a slog. It’s sort of like trying to read Chaucer, although of course Hebrew isn’t descended from Aramaic like Modern English is from middle English.

3

Nitpick: Tanakh, not Torah. Only one word in the Torah is Aramaic, a place name. Of the three divisions of the Hebrew Bible, most of the Aramaic passages occur in the third set, Khetuvim, “the Writings”, as opposed to Torah and Neba’im, “the Prophets”. (The Book of Jeremiah, with one quoted Aramaic sentence, is included in Neba’im, but Daniel is in Khetuvim, as is Ezra, the other Bible book with extensive Aramaic sections.

4

Studying Aramaic isn’t that uncommon for religious Jews. When I studied (at a secular university) in Israel, my roommate, who was from suburban New Jersey and had attended Jewish day school for her entire life, had studied Aramaic as a regular part of her coursework.

The Talmud is written largely in Aramaic, which is why people bother to study it.

5

My father was educated at Yeshiva through 12th grade, and reads Aramaic. I think its pretty much par for the course.