Hi, I learned that if you are not able to do certain things before Shkiah, then after the fact you can still daven Mincha or wash for seudah shlishit. How long is this window? I heard various opinions such as 9-13 minutes after Shkia.

Shalom, One should certainly make every effort to do that which is required to do before shkiah by sunset. However in times of need, especially after the fact when you missed shkiah, there are opinions to rely upon to do certain things even after shkiah. (My answer to you is based on the accepted practice in Israel to figure out halachic times based on the Gaonim - but those who hold like Rabbainu Tam (certain Hassidim, especially outside Israel), the times will be very different). Mincha may be recited during the sunset period before nightfall (Bein Hashmashot), which is 13.5 - 18 minuets after sunset. The third meal on Shabbat may likewise be started during this time frame. Some Rabbis hold the stricter 13.5 minuet opinion, and others hold up to 18 minuets. Let me stress again that major halachic opinions reject this idea alltoghter and forbid saying Mincha or starting the third meal after the sun has droped below the horizen (shkiah). One must make every effort to complie with that ruling. Blessings