I can't really say for sure about "――" without more context. My guess is that 横線 is being pulled out to make it clear that it's the term being explained (maybe it's part of a list?). The technical terms in my translation might be off, but this should give you the feel:
The Horizontal Line -- that blue thing which goes by the name of ....
You might have been thrown off by 青いそれ, literally "blue that". In English, demonstrative pronouns cannot be modified by adjectives, but that is not the case in Japanese.
Basically it says that this is "the result of" visualizing your remaining life. Since it is the result of that process, it's already complete, therefore した.
A subtle point is that もの is not the subject of the relative clause. I.e. the literal translation of 俺の生命の残量を可視化したもの is not "The thing that visualizes my remaining life" (although that might be the most idiomatic English expression), rather "(The thing which is) the result of having visualized my remaining life". Note that Japanese is very flexible about the role of the modified noun in the relative clause. Less so in English, which is why the literal translation I give above does not involve a relative clause at all.
The technical way to explain した would be say that this is not a past tense, but a perfective aspect. The use of different verb forms for tense-aspect in Japanese is quite subtle, and the use differs between matrix sentences and subordinate/relative clauses. Let me know if you want to know more about this, it might be worth a separate question.