自分を理解してくれる者がいる is an idea ("There is someone who understands you"). 者 just means "person(s)" and even though it is rarely used in real life these days, let us leave it as is since OP says this is a line from a comic.
In order to use an idea as a topic in Japanese, we need to nominalize it. The easiest way to do so INFORMALLY is to add a の, which is done here. Since we now have a "virtual noun", we can add the topic-marker は. The author could have said:
自分を理解してくれる者がいるのは～～ but he wanted to make it sound more formal and emphatic, so he used という and said:
自分を理解してくれる者がいるというのは～～ In essence, he expressed the formality and emphasis that he desired by "quoting" the idea --- by treating it as a written saying from somewhere.
One sees the same process in the phrase 一人というのは. One may wonder how 一人 could be an idea but here it is the same as 一人でいる or 理解してくれる人がいない.
OP was not successful in reading the structure of the last sentence. It does not say "I did not understand myself." Rather it says, "I used to be 苛まれた by the 孤独 that came from the fact that 自分を理解する者がいない."
"That there is someone who understands you is a pleasant thing. Being alone must have felt lonely, I presume? I, too, used to be tormented by the solitariness of not having anyone to understand me."