Yes dear, day 11 is quite fertile for many women. You can track your natural body temp and cervical mucus to know. But if you have any unusual pain or spotty bleeding along with it, please check with your doctor instead of guessing.
Yes, conceiving around day 11 is highly possible because sperm can live inside for a few days. I conceived early in my cycle too! My journey ended with a C-section and the recovery was quite tough, so please take care of your body from day one if you are planning.
It actually depends on your cycle length, so it is best to ask your gynac clearly. When I had doubts about my fertile window, the hospital counselor gave me a proper chart to track. They explain all this so well.
Yes, day 11 is very close to ovulation, especially if your cycle is around 25-28 days. In my case, my cycle was all over the place due to thyroid, so regular doctor follow-ups and blood tests were a must for tracking. Do consult your doctor once.