Aurora, sorry that I’m responding after the times for the Selichos in your part of the world. As a matter of fact, many women do go for the first night of Selichos, not usually past this point, although it is definitely not unheard of. My daughter went most of the nights a few years ago. She was even allowed to come to school late if I sent a note with her.
As far as saying the Selichos prayers at home, there are many parts that are possible to say, but I am under the impression that the parts regarding the 13 Attributes of H-Shem are not to be said unless one is present in a minyan (quorum) of men. Artscroll probably has some of the laws regarding this in the back of the prayer books for these special prayers.
I do, however, think as a first step that it would be perfectly fine for you to start off by saying these prayers at home especially since you’ve said that you’re far from an Orthodox community. As an older single in the past, when I would make my Shabbos plans for the Shabbos when Selichos would begin that night, I would ask my host if I could stay over until Sunday morning so that I could be nearby for the Selichos as well. It was never a problem, so perhaps next year you’ll be able to do that.
Just as an aside, I read in another post that you feel you are of an age that you might never get married, you might actually find that getting married at an older age is still possible in the Orthodox world. Men are encouraged to be married as it says in the Torah that it is “not good for a man to be alone”, and I know of one rabbi who got married again recently and he is over the age of 85, so you never know.
Wishing you a meaningful New Year in your path to Torah and Mitzvos.