1) One who cannot make it to Shul (or one who came late, and missed the minyan) may say Selichos on his own. However, the "Sh’losh Esrei Middos- the Tefilah enumerating the 13 attributes of Hashem’s mercy" as well as any Selichos that mention them (e.g. U’Zchor Lanu HaYom Bris Sh’losh Esrei...") may not be said without a Minyan.  

However, if they are read with the tune (Trup) used to read the Torah, then they may be said.

Women who say Selichos at home, should never say the Sh’losh Esrei Middos, as they aren’t usually familiar with the tune used to read the Torah (Psak of Rav Yosef Shalom Elyashiv Shlita)

Likewise, any parts of the Selichos that are written in Aramaic (e.g.  Machei U’Masei..., Maran Di B’Shmaya...) should not be said without a Minyan. Saying these with the tune used for Torah reading wouldn’t help, as they aren’t Pesukim in the Torah.

One who is an Avel (a mourner during the first week after the passing of a close relative) may not leave his home to go to Shul for Selichos, and should recite it alone, or with a Minyan that comes to his home. ( except for Erev Rosh Hashana, when he may go to Shul, if he cannot get a Minyan to come to his home).

 
2) Certain women have the custom , following  the opinion of the Rama, not to enter a Shul when they are in a state of  Niddah. According to the Gaon of Vilna a Niddah is never prohibited from davening and/or entering a Shul.