Do we know more about Kara through her supporting cast?

The question is a little misleading. It can be answered a number of ways and only touches the surface of who Kara was, is, and will become.

Firstly, the supporting characters and their associated storylines in S2 have been more prominent and provide additional dimension to each one in a variety of ways. Not all of these ways have to or should involve Kara. For example, Alex, James, J'onn and Winn have separate yet interweaving storylines that stand on their own without Kara's presence. This is a good thing. It allows the viewer to formulate a clearer picture of each character outside of the main narrative and adds a 3-D real-life dimension to each.

Secondly, Kara has matured to a point in which she is not overly-reliant on the supporting cast to continually come to her rescue or to make / take decisions on her behalf or for her perceived best self-interest. If you look at the arc S1 to now, the character has grown and more fully embraced her role and mission and has developed a more adult outlook (i.e. it has become more complicated, nuanced, and much less straightforward than in S1) and she now takes decisions in a more mature manner.

Thirdly, the occasional supporting characters such as Mon-EL, Lena, Cat, Jeremiah, Eliza, Snapper and others have also helped shape Kara's journey in that each one brings a small, yet valuable piece to the overall puzzle. The reason I mention Cat as an occasional supporting character is that her role in S1 was that of a mentor and was much more prominent, in S2 that has largely disappeared and the advice, encouragement and sounding board aspects that Cat brought to the table is more self-generated (it comes from within Kara rather than from others). This, too, is also a good thing.

Finally, we can endlessly debate the merits and drawbacks of each character, their portrayals, their relevance and the like, and how they interact and impact Kara's overall journey but one thing is very obvious, Kara is a more self-reliant and self-assured character in S2 and will continue to evolve as mainstay and new characters are put into the mix.

What I expect to ultimately happen is to see more complexity, more joy, more heartache, more character interactions (large and small), many uncertain trials and tribulations and more self-realisation as the Supergirl story progresses.

Wow Romulus very well said and if I may add

Firstly, the supporting characters and their associated storylines in S2 have been more prominent and provide additional dimension to each one in a variety of ways. Not all of these ways have to or should involve Kara. For example, Alex, James, J'onn and Winn have separate yet interweaving storylines that stand on their own without Kara's presence. This is a good thing. It allows the viewer to formulate a clearer picture of each character outside of the main narrative and adds a 3-D real-life dimension to each

I am so glad the EPs let Alex get a life. The character would have become boring and two dimensional if things had stayed as they were in S1. To bring it back to Kara, Alex having a live also allows Kara to have a life. Last season Winn was what my college girlfriends and I would call Kara's "monkey boy". A "monkey boy" was a guy who liked us but we didn't like him and to varying degrees (from simply knowing that if we did change our mind he would come running to stringing him along) exploited that. Kara was nothing but kind to Winn but we all knew in she had said she changed her mind he would have said yes mam. Winn is not Kara's "monkey boy" anymore and thank goodness for that.

Secondly, Kara has matured to a point in which she is not overly-reliant on the supporting cast to continually come to her rescue or to make / take decisions on her behalf or for her perceived best self-interest. If you look at the arc S1 to now, the character has grown and more fully embraced her role and mission and has developed a more adult outlook (i.e. it has become more complicated, nuanced, and much less straightforward than in S1) and she now takes decisions in a more mature manner.

Right in the beginning she really did need help and got just what she needed. Cat and James particularly helped her gain confidence and hone her moral compass. Cat helped her define who Supergirl is. Alex provided emotional support as well as training. J'onn helped her learn discipline while she tought him to laugh again.

Thirdly, the occasional supporting characters such as Mon-EL, Lena, Cat, Jeremiah, Eliza, Snapper and others have also helped shape Kara's journey in that each one brings a small, yet valuable piece to the overall puzzle. The reason I mention Cat as an occasional supporting character is that her role in S1 was that of a mentor and was much more prominent, in S2 that has largely disappeared and the advice, encouragement and sounding board aspects that Cat brought to the table is more self-generated (it comes from within Kara rather than from others). This, too, is also a good thing.

Last season Kara went to others particularly Cat with all her problems before really trying to solve them herself. That was fine last season because she did need Cat's advice but if that had continued Kara's growth as a person would have been stunted. If Cat were still around this season we would have gotten lots of her saying figure it out yourself Kara. The balcony of deep thoughts is almost entirely missing because Kara simply doesn't need it anymore.

Finally, we can endlessly debate the merits and drawbacks of each character, their portrayals, their relevance and the like, and how they interact and impact Kara's overall journey but one thing is very obvious, Kara is a more self-reliant and self-assured character in S2 and will continue to evolve as mainstay and new characters are put into the mix.

Kara's saved her world and this season helped save another world. No way would she be the same person or need the same support she did in the beginning which means she can support others too. Kara's grown so everyone around her had to grow too.