How does UK Visa application define a dependent?
It doesn't. These types of questions reveal one of the strategies in drafting the rules; they are vague in some places by design and intent. There is no precise definition for "dependent" in the corpus of the visitor rules, and even august authorities that nail down everything like MacDonald and Clayton do not offer precision about the term "dependent" (within the visitor domains).
So in the absence of a definition with a legislative pedigree, we have to resort to the 'best practices' advice for the generic case covering all ambiguities:
use the natural meaning of the words as they pertain to your own situation.
I'm not sure in which one should I fill up our details.
You select the most appropriate according to how you interpret "dependent" and proceed. If you have doubts, you can complete both sections. They are not going to refuse on grounds of filling out the wrong section as long as all the information is represented somewhere. Take care that there's a HUGE risk of refusal because your father is trying to take two adults with no palpable ties to their home country who may follow the pattern of going underground and making foreign remittances to their family (and I'm guessing that will be the outcome, but that's just a guess). It means you may be focusing on the wrong things.
In both cases, what supporting documents would we need in our
Happily, the answer here is canonically clear. It's spelled out in the guidance documents: Vaf1 Guidance Notes and the Supporting Documents Guidance. Everything is there (with some exceptions noted here). Also canonically, if you are worried about the quality of your evidence, stay off the net and arrange a consultation with a licensed solicitor.
Note that "child" on the other hand, is the subject of both legislation and international treaties. It is a minor 18 and under. In terms of claiming a child, the simplest case is where both distaff and spear side lineage is explicitly identified on the birth certificate, but many more complex cases are acceptable to ECO's. Standard Visitor Visa applications will fail if the lineage is unclear, and unknowing parents have been snagged with refusals they were not expecting.