Shuurei from the begining wanted to achieve something big and with Ryuki's help she was able governor test which women were not allowed to take and became co-governor of Sa province. If I remeber correctly she had an interest in Seiran her adopted brother who later is known to be also Ryuki's older half brother. Seiran known Shurei since she was a child and is very protective of Shurei. I think it ends after Shurei stabilizes Sa province as co-governor and the one by her side at the time is Seiran. This is assuming the anime covered all the novels before hand. If not it covered atleast 13-14 novels. Manga version still has a long way to go.

It's complex. There is romance between Ryuuki and Shurei, but she can't have children, so she pushes him away. Sorry if that's a spoiler, but that's piece of the plot - Why she feels Ryuuki should give up on her and marry someone else. But, I read a translation of a recent light novel. She did tell Ryuuki about it and she agreed to marry him, but he would have to agree to have a concubine have his heir. Over the series, she does have many men after her affections, but she ignores them all - pretty much.

in the 18th novel, Shuurei will eventually marry Ryuuki. The next year it reads that she will die in childbith ; she was only 30 years old...

the end is very sad!

She became a government official which was not given to females through the same means any male would achieve it. Using all her knowledge she passed the test for government officials (if I remeber correctly it was a very very good score) proving to everyone women are just as capable.