How to list down actions that are done in the past and are still being done in the present?

Solution 1:

Most of your sentence consists of a series of four actions linked to the same base. If you repeat the word have in each phrase, then all four actions link directly to the word I. On the other hand if you use the word have only once—immediately after I—then the four actions link directly to have.

In other words, the parallel phrases can branch out from "I":

have conquered sleepless nights,

have studied various topics

have participated in extra-curricular activities, and

have juggled my time for school and home duties

Or they can branch out from "I have":

conquered sleepless nights,

studied various topics,

participated in extra-curricular activities, and

juggled my time for school and home duties

Either way, the phrases are properly in parallel; but unless you want to emphasize the word have for some reason, you can save a little space and spare your readers a little repetition by using "I have" rather than "I" as the base.