I don't understand where this is going, why did she kiss her?

I don't know either, I just know that I liked it :p

Because she loves her. This entire chapter is entirely about her inner thought process coming to the conclusion that she loves Sumika. Next chap will probably give further clarity, but I suspect she's started to realize that her idea of romance was naive.

Loving someone deeply is wanting to make them happy. It's when their happiness makes you happy. The strongest relationships are the partnerships where both participants are motivated by a desire to enrich each *others* lives.

Yeah nah, doubt it. By telling her to keep loving her she’s just leading Sumika on.